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re: talk:Tree of primitive Pythagorean triples

from talk:Tree of primitive Pythagorean triples&direction=prev&oldid=906435953 Gangleri 217.86.249.144 (talk) 12:15, 16 July 2019 (UTC)

Dual representation for the tree

1 0 1 1 0	3 4 5 2 1	5 12 13 3 2	7 24 25 4 3	9 40 41 5 4
				105 88 137 11 4
				91 60 109 10 3
			55 48 73 8 3	105 208 233 13 8
				297 304 425 19 8
				187 84 205 14 3
			45 28 53 7 2	95 168 193 12 7
				207 224 305 16 7
				117 44 125 11 2
		21 20 29 5 2	39 80 89 8 5	57 176 185 11 8
				377 336 505 21 8
				299 180 349 18 5
			119 120 169 12 5	217 456 505 19 12
				697 696 985 29 12
				459 220 509 22 5
			77 36 85 9 2	175 288 337 16 9
				319 360 481 20 9
				165 52 173 13 2
		15 8 17 4 1	33 56 65 7 4	51 140 149 10 7
				275 252 373 18 7
				209 120 241 15 4
			65 72 97 9 4	115 252 277 14 9
				403 396 565 22 9
				273 136 305 17 4
			35 12 37 6 1	85 132 157 11 6
				133 156 205 13 6
				63 16 65 8 1

Hi! The table above combines the representation of the primitive Pythagorean triplets with the values of the primitive pair of integers generating them.
The table includes as additional root the trivial triplet (1, 0, 1) which is generated by the (m, n) pair (1, 0). Please note that all (m, n) pairs are written with m < n which is the opposite of the requirement described in the article.
The alternative calculations of the childs of any Pythagorean triplet are as follow:

up: (m_new, n_new) = (2m-n, m)

Pell pair: (m_new, n_new) = (2m+n, m)

for (m, n) other then (1, 0) down: (m_new, n_new) = (m+2n, n)

note: from (1, 0) both the up path and the "Pell" path generate the same main root value (2, 1)

The calculations of the triplet childs might be simpler as using matrix calculations. Please note that both the up way and the "Pell" way are preserving m, the greater value of the (m, n) pair, while the down way preserves n, the smaller value of the (m, n) pair.
Additional remark on the Pell numbers: The sequence consists of values of the hypotenuse of a Pythagorean triplet followed by its circumference (a+b+c). It starts with 1 and 2. This pair generates the triplet (3, 4, 5) so both 5 and 12 = 3 + 4 + 5 can be added to the sequence. By using (2, 5) one generates the triplet (21, 20, 29) so both 29 and 70 = 21 + 20 +29 can be added to the sequence. Nevertheless (5, 12) is the next pair to be used on the "Pell" path.
Best regards Gangleri

The triplet (0, 1, 1) generated by the (1, 0) pair does not have a parent Pythagorean triplet.

In order to calculate the parent of a distinct arbitrary primitive Pythagorean triplet (a, b, c) first one must identify the generating (m, n) pair which is generating the examined Pythagorean triplet. The pair is identified via

m=square root(c²-a²)/2 and because m is not zero for triples other then (0, 1, 1) n=b/2m

algorithm:

note: the case for n=0 is discussed above

if m-2n=0 then the analysed Pythagorean triplet is the main root Pythagorean triplet (3, 4, 5)

if m-2n<0 then (m_new, n_new) = (n, 2n-m) and the way was "up"

else if n>m-2n then (m_new, n_new) = (n, m-2n) and the way was the "Pell" way

else (m_new, n_new) = (m-2n, n) and the way was "down".

Regards Gangleri — Preceding unsigned comment added by 2A02:810D:41C0:134:5D5D:FEFD:1D74:D8AF (talk) 12:22, 6 July 2019 (UTC)

Switched to (m, n) with m > n representation. Regards Gangleri 13:46, 7 July 2019 (UTC)

Hopping on the Pell path

Any two consecutive numbers of the Pell series P_k = n and P_{k + 1} = m generate a Pythagorean triplet (a, b, c). The (m, n) pair is used to generate (m² - n², 2mn, m² + n²) with the additional property that | a - b | = 1. Take p = 2m² + 2mn the circumference of the triangle and q = m² + n² the hypotenuse of the triangle.
With (p, q) a new Pythagorean triplet can be generated having an interesting circumference and an interesting hypotenuse.
Now consider the iteration p_new = 2p² + 2pq the circumference and q_new = p² + q² the hypotenuse. These are two different consecutive numbers of the Pell series so they generat a Pythagorean triplet with | a - b | = 1.
Examples:

(P₂, P₁) i.e. (2, 1) iterates to

(P₄, P₃) i.e. (12, 5) iterates to

(P₈, P₇) i.e. (408 169) iterates to

(P₁₆, P₁₅) i.e. (470832 195025) iterates to

(P₃₂, P₃₁) i.e. (627013566048 259717522849)

Best regards Gangleri 18:42, 7 July 2019 (UTC) — Preceding unsigned comment added by 2A02:810D:41C0:134:F81F:7483:C15A:1780 (talk)

What are neither coincidences nor obvious for any two consecutive numbers of the Pell series (P_n, P_{n - 1}) are properties for their generated Pythagorean triangle (a, b, c)

i) c is a Pell number

ii) a + b + c is a Pell number too

iii) a + b + c is the successor of c in the Pell series

Best regards Gangleri 20:33, 7 July 2019 (UTC)

Note that the predecessor of the Pell number c can be calculated directly as a + b - c. So (c, a + b - c) can be used as a pair of two consecutive Pell numbers witch differs from the original (m, n) if that was not (1, 0).
Because of this relation an additional hopping path can be used in order to find two consecutive Pell numbers. From P_k = n and P_{k + 1} = m we use the hypotenuse c of the generated Pythagorean triangle and its predecessor a + b - c using the formulas

m_new = m² + n²

n_new = 2mn - 2n²

Examples:

(P₂, P₁) i.e. (2, 1) iterates to

(P₃, P₂) i.e. (5, 2) iterates to

(P₅, P₄) i.e. (29 12) iterates to

(P₉, P₈) i.e. (985 408) iterates to

(P₁₇, P₁₆) i.e. (1136689 470832)

Conclusion: Together with the original Pell iteration P_n = P_{n - 1} + 2P_{n - 2} (for n >=2 ) there are tree paths from one pair of consecutive Pell numbers other then (1, 0) to another pair of consecutive Pell numbers.
Best regards Gangleri 09:37, 8 July 2019 (UTC)

Trees and their objects

examples

Berggrens's	Price's
0,113313 1643 924 1885 42 11 53 31 4452 682	1,22212 1643 924 1885 42 11 53 31 4452 682
0,131331 1235 1932 2293 42 23 65 19 5460 874	to be calculated 1235 1932 2293 42 23 65 19 5460 874 1,113213
to be calculated 1695 6272 6497 64 49 113 15 14464 1470 0,11123111	1,33233 1695 6272 6497 64 49 113 15 14464 1470
0,122222 23661 23660 33461 169 70 #Pell(7,6) 239 99 80782 13860	to be calculated 23661 23660 33461 169 70 #Pell(7,6) 239 99 80782 13860 1,11132111121

Each primitive Pythagorean triplet can be identified by one of the following key values:

a) generating method for an arbitrary primitive Pythagorean triplet and the path to that triplet; because only two exhausting methods are known this could be either one of

a1) Berggrens's method and the path to the triplet in the Berggrens's tree as "0,11213" used below

a2) Price's method and the path to the triplet in the Price's tree as "1,2232" used below

or both

b) triplet values as (a, b, c) where a and c are odd integer numbers and b is an even integer number which might be zero; gcd(a, b, c) = 1 and a, b and c fullfill the Pythagorean equation a² + b² = c²; triplets not obeing the Pythagorean equation are not discussed in the following

c) the generating pair (m, n) where m and n are integer numbers m > n >= 0 and gcd(m, n) = 1 generating the primitive Pythagorean triplet (a, b, c) with the set of formulas 1 ; any artitrary pair (m, n) with the properties from above identifies a unique primitive Pythagorean triplet

d) the generating pair (u, v) where u and v are integer numbers u > v and both values are odd and gcd(u, v) = 1 and they generate the same primitive Pythagorean triplet (a, b, c) with the set of formulas 2 ; any artitrary pair (m, n) with the properties from above identifies a unique primitive Pythagorean triplet

e) the pair (p, l) formed by the numerical values of the perimeter and "lead" for a triangle formed by a primitive Pythagorean triplet (a, b, c) ; the lead of the sum of the length of the two legs of the associated Pythagorean triangle to the length of the hypotenuse of the Pythagorean triangle;
please note the relations p = a + b + c and l = a + b - c as well as c = (p - l) / 2 ; both p and l are even numbers; there are pairs of (p, l) which do neiter relate to primitive Pythagorean triplet nor to general Pythagorean triplet; this means that (p, l) can not be selected randomly

The necessary calculations / formulas to determine the four other associated key values when one key is known will be described in the detail subparagraphs.
Notes: The perimeters of two triangles associated to two different Pythagorean triplets might have the same values as can be seen searching for the hashtags "#p1a" to "#p3a" and "#p1b" to "#p5b" in the following two tables.

Berggrens's tree

Berggrens's tree

all generations (0 to 6)
0 0 1 0 1 1 0 #Plato(0) #Pell(1,0) n/a 2 0	0,1 1 3 4 5 2 1 #Plato(1) #Pythagoras(1) #Pell(2,1) 3 1 4 4 12 2	0,11 5 12 13 3 2 #Plato(2) 5 1 12 9 30 4	0,111 7 24 25 4 3 #Plato(3) 7 1 24 16 56 6	0,1111 9 40 41 5 4 #Plato(4) 9 1 40 25 90 8	0,11111 1,13 11 60 61 6 5 #Plato(5) 11 1 60 36 132 10	0,111111 1,31 13 84 85 7 6 #Plato(6) 13 1 84 49 182 12
						0,111112 253 204 325 17 6 23 11 204 289 782 132
						0,111113 231 160 281 16 5 21 11 160 256 672 110
					0,11112 1,1212 171 140 221 14 5 19 9 140 196 532 90	0,111121 333 644 725 23 14 37 9 644 529 1702 252
						0,111122 893 924 1285 33 14 47 19 924 1089 3102 532
						0,111123 551 240 601 24 5 29 19 240 576 1392 190
					0,11113 1,11211 153 104 185 13 4 17 9 104 169 442 72	0,111131 315 572 653 22 13 35 9 572 484 1540 234
						0,111132 731 780 1069 30 13 43 17 780 900 2580 442
						0,111133 425 168 457 21 4 25 17 168 441 1050 136
				0,1112 1,3211 105 88 137 11 4 15 7 88 121 330 56	0,11121 1,3212 203 396 445 18 11 29 7 396 324 1044 154	0,111211 301 900 949 25 18 43 7 900 625 2150 252
						0,111212 1885 1692 2533 47 18 65 29 1692 2209 6110 1044
						0,111213 1,11222 1479 880 1721 40 11 51 29 880 1600 4080 638
					0,11122 555 572 797 26 11 37 15 572 676 1924 330	0,111221 1,31221 1005 2132 2357 41 26 67 15 2132 1681 5494 780
						0,111222 3293 3276 4645 63 26 89 37 3276 3969 11214 1924
						0,111223 2183 1056 2425 48 11 59 37 1056 2304 5664 814
					0,11123 345 152 377 19 4 23 15 152 361 874 120	0,111231 795 1292 1517 34 19 53 15 1292 1156 3604 570
						0,111232 1403 1596 2125 42 19 61 23 1596 1764 5124 874
						0,111233 713 216 745 27 4 31 23 216 729 1674 184
				0,1113 91 60 109 10 3 13 7 60 100 260 42	0,11131 1,1221 189 340 389 17 10 27 7 340 289 918 140	0,111311 287 816 865 24 17 41 7 816 576 1968 238
						0,111312 1,22122 1647 1496 2225 44 17 61 27 1496 1936 5368 918
						0,111313 1,22321 1269 740 1469 37 10 47 27 740 1369 3478 540
					0,11132 429 460 629 23 10 33 13 460 529 1518 260	0,111321 767 1656 1825 36 23 59 13 1656 1296 4248 598
						0,111322 2607 2576 3665 56 23 79 33 2576 3136 8848 1518
						0,111323 1749 860 1949 43 10 53 33 860 1849 4558 660
					0,11133 247 96 265 16 3 19 13 96 256 608 78	0,111331 585 928 1097 29 16 45 13 928 841 2610 416
						0,111332 969 1120 1481 35 16 51 19 1120 1225 3570 608
						0,111333 475 132 493 22 3 25 19 132 484 1100 114
			0,112 55 48 73 8 3 11 5 48 64 176 30	0,1121 1,12111 105 208 233 13 8 21 5 208 169 546 80	0,11211 1,12113 155 468 493 18 13 31 5 468 324 1116 130	0,112111 1,12131 205 828 853 23 18 41 5 828 529 1886 180
						0,112112 2077 1764 2725 49 18 67 31 1764 2401 6566 1116
						0,112113 1767 1144 2105 44 13 57 31 1144 1936 5016 806
					0,11212 987 884 1325 34 13 47 21 884 1156 3196 546	0,112121 1869 3740 4181 55 34 89 21 3740 3025 9790 1428
						0,112122 5405 5508 7717 81 34 115 47 5508 6561 18630 3196
						0,112123 3431 1560 3769 60 13 73 47 1560 3600 8760 1222
					0,11213 777 464 905 29 8 37 21 464 841 2146 336	0,112131 1659 2900 3341 50 29 79 21 2900 2500 7900 1218
						0,112132 3515 3828 5197 66 29 95 37 3828 4356 12540 2146
						0,112133 1961 720 2089 45 8 53 37 720 2025 4770 592
				0,1122 297 304 425 19 8 27 11 304 361 1026 176	0,11221 539 1140 1261 30 19 49 11 1140 900 2940 418	0,112211 781 2460 2581 41 30 71 11 2460 1681 5822 660
						0,112212 5341 4740 7141 79 30 109 49 4740 6241 17222 2940
						0,112213 4263 2584 4985 68 19 87 49 2584 4624 11832 1862
					0,11222 1755 1748 2477 46 19 65 27 1748 2116 5980 1026	0,112221 3213 6716 7445 73 46 119 27 6716 5329 17374 2484
						0,112222 10205 10212 14437 111 46 157 65 10212 12321 34854 5980
						0,112223 6695 3192 7417 84 19 103 65 3192 7056 17304 2470
					0,11223 1161 560 1289 35 8 43 27 560 1225 3010 432	0,112231 2619 4340 5069 62 35 97 27 4340 3844 12028 1890
						0,112232 4859 5460 7309 78 35 113 43 5460 6084 17628 3010
						0,112233 2537 816 2665 51 8 59 43 816 2601 6018 688
				0,1123 1,2112 187 84 205 14 3 17 11 84 196 476 66	0,11231 429 700 821 25 14 39 11 700 625 1950 308	0,112311 671 1800 1921 36 25 61 11 1800 1296 4392 550
						0,112312 3471 3200 4721 64 25 89 39 3200 4096 11392 1950
						0,112313 2613 1484 3005 53 14 67 39 1484 2809 7102 1092
					0,11232 765 868 1157 31 14 45 17 868 961 2790 476	0,112321 1,12223 1343 2976 3265 48 31 79 17 2976 2304 7584 1054
						0,112322 4815 4712 6737 76 31 107 45 4712 5776 16264 2790
						0,112323 3285 1652 3677 59 14 73 45 1652 3481 8614 1260
					0,11233 391 120 409 20 3 23 17 120 400 920 102	0,112331 969 1480 1769 37 20 57 17 1480 1369 4218 680
						0,112332 1449 1720 2249 43 20 63 23 1720 1849 5418 920
						0,112333 667 156 685 26 3 29 23 156 676 1508 138
			0,113 45 28 53 7 2 9 5 28 49 126 20	0,1131 95 168 193 12 7 19 5 168 144 456 70	0,11311 1,2211 145 408 433 17 12 29 5 408 289 986 120	0,113111 1,2213 195 748 773 22 17 39 5 748 484 1716 170 #p1a
						0,113112 1827 1564 2405 46 17 63 29 1564 2116 5796 986
						0,113113 1537 984 1825 41 12 53 29 984 1681 4346 696
					0,11312 817 744 1105 31 12 43 19 744 961 2666 456	0,113121 1539 3100 3461 50 31 81 19 3100 2500 8100 1178
						0,113122 4515 4588 6437 74 31 105 43 4588 5476 15540 2666
						0,113123 2881 1320 3169 55 12 67 43 1320 3025 7370 1032
					0,11313 627 364 725 26 7 33 19 364 676 1716 266 #p1a	0,113131 1,23221 1349 2340 2701 45 26 71 19 2340 2025 6390 988
						0,113132 2805 3068 4157 59 26 85 33 3068 3481 10030 1716
						0,113133 1,21232 1551 560 1649 40 7 47 33 560 1600 3760 462
				0,1132 1,322 207 224 305 16 7 23 9 224 256 736 126	0,11321 369 800 881 25 16 41 9 800 625 2050 288	0,113211 531 1700 1781 34 25 59 9 1700 1156 4012 450
0,113212 3731 3300 4981 66 25 91 41 3300 4356 12012 2050
0,113213 2993 1824 3505 57 16 73 41 1824 3249 8322 1312
0,11322 1265 1248 1777 39 16 55 23 1248 1521 4290 736	0,113221 2323 4836 5365 62 39 101 23 4836 3844 12524 1794
	0,113222 7315 7332 10357 94 39 133 55 7332 8836 25004 4290
	0,113223 4785 2272 5297 71 16 87 55 2272 5041 12354 1760
0,11323 851 420 949 30 7 37 23 420 900 2220 322	0,113231 1909 3180 3709 53 30 83 23 3180 2809 8798 1380
	0,113232 3589 4020 5389 67 30 97 37 4020 4489 12998 2220
	0,113233 1887 616 1985 44 7 51 37 616 1936 4488 518
0,1133 1,1121 117 44 125 11 2 13 9 44 121 286 36	0,11331 279 440 521 20 11 31 9 440 400 1240 198	0,113311 441 1160 1241 29 20 49 9 1160 841 2842 360
		0,113312 2201 2040 3001 51 20 71 31 2040 2601 7242 1240
		0,113313 1,22212 1643 924 1885 42 11 53 31 924 1764 4452 682
	0,11332 455 528 697 24 11 35 13 528 576 1680 286	0,113321 793 1776 1945 37 24 61 13 1776 1369 4514 624
		0,113322 2905 2832 4057 59 24 83 35 2832 3481 9794 1680
		0,113323 1995 1012 2237 46 11 57 35 1012 2116 5244 770
	0,11333 221 60 229 15 2 17 13 60 225 510 52	0,113331 559 840 1009 28 15 43 13 840 784 2408 390
		0,113332 799 960 1249 32 15 47 17 960 1024 3008 510
		0,113333 357 76 365 19 2 21 17 76 361 798 68
0,12 1,21 21 20 29 5 2 #Pell(3,2) 7 3 20 25 70 12	0,121 39 80 89 8 5 13 3 80 64 208 30	0,1211 57 176 185 11 8 19 3 176 121 418 48	0,12111 75 308 317 14 11 25 3 308 196 700 66	0,121111 93 476 485 17 14 31 3 476 289 1054 84
				0,121112 1,32321 1325 1092 1717 39 14 53 25 1092 1521 4134 700
				0,121113 1,32122 1175 792 1417 36 11 47 25 792 1296 3384 550
			0,12112 779 660 1021 30 11 41 19 660 900 2460 418	0,121121 1501 2940 3301 49 30 79 19 2940 2401 7742 1140
				0,121122 4141 4260 5941 71 30 101 41 4260 5041 14342 2460
				0,121123 2583 1144 2825 52 11 63 41 1144 2704 6552 902
			0,12113 665 432 793 27 8 35 19 432 729 1890 304	0,121131 1387 2484 2845 46 27 73 19 2484 2116 6716 1026
				0,121132 3115 3348 4573 62 27 89 35 3348 3844 11036 1890
				0,121133 1785 688 1913 43 8 51 35 688 1849 4386 560
		0,1212 377 336 505 21 8 29 13 336 441 1218 208	0,12121 715 1428 1597 34 21 55 13 1428 1156 3740 546	0,121211 1053 3196 3365 47 34 81 13 3196 2209 7614 884
				0,121212 6765 6052 9077 89 34 123 55 6052 7921 21894 3740
				0,121213 5335 3192 6217 76 21 97 55 3192 5776 14744 2310
			0,12122 2059 2100 2941 50 21 71 29 2100 2500 7100 1218	0,121221 3741 7900 8741 79 50 129 29 7900 6241 20382 2900
				0,121222 12141 12100 17141 121 50 171 71 12100 14641 41382 7100
				0,121223 8023 3864 8905 92 21 113 71 3864 8464 20792 2982
			0,12123 1305 592 1433 37 8 45 29 592 1369 3330 464	0,121231 2987 4884 5725 66 37 103 29 4884 4356 13596 2146
				0,121232 5355 6068 8093 82 37 119 45 6068 6724 19516 3330
				0,121233 2745 848 2873 53 8 61 45 848 2809 6466 720
		0,1213 299 180 349 18 5 23 13 180 324 828 130	0,12131 637 1116 1285 31 18 49 13 1116 961 3038 468	0,121311 975 2728 2897 44 31 65 13 2728 1936 6600 806
				0,121312 5439 4960 7361 80 31 111 49 4960 6400 17760 3038
				0,121313 4165 2412 4813 67 18 85 49 2412 4489 11390 1764
			0,12132 1,32221 1357 1476 2005 41 18 59 23 1476 1681 4838 828	0,121321 2415 5248 5777 64 41 105 23 5248 4096 13440 1886
				0,121322 8319 8200 11681 100 41 141 59 8200 10000 28200 4838
				0,121323 5605 2772 6253 77 18 u 105 2772 5929 14630 2124
			0,12133 759 280 809 28 5 33 23 280 784 1848 230	0,121331 1817 2856 3385 51 28 79 23 2856 2601 8058 1288
				0,121332 2937 3416 4505 61 28 89 33 3416 3721 10858 1848
				0,121333 0,12312 1419 380 1469 38 5 43 33 380 1444 3268 330
	0,122 1,122 119 120 169 12 5 #Pell(4,3) 17 7 120 144 408 70	0,1221 1,21211 217 456 505 19 12 31 7 456 361 1178 168	0,12211 315 988 1037 26 19 45 7 988 676 2340 266	0,122111 413 1716 1765 33 26 59 7 1716 1089 3894 364
				0,122112 4365 3692 5717 71 26 97 45 3692 5041 13774 2340
				0,122113 3735 2432 4457 64 19 83 45 2432 4096 10624 1710
			0,12212 2139 1900 2861 50 19 69 31 1900 2500 6900 1178 #p2a	0,122121 4061 8100 9061 81 50 131 31 8100 6561 21222 3100
				0,122122 11661 11900 16661 119 50 169 69 11900 14161 40222 6900
				0,122123 7383 3344 8105 88 19 107 69 3344 7744 18832 2622
			0,12213 1705 1032 1993 43 12 55 31 1032 1849 4730 744	0,122131 3627 6364 7325 74 43 117 31 6364 5476 17316 2666
				0,122132 7755 8428 11453 98 43 141 55 8428 9604 27636 4730 #p3a
				0,122133 4345 1608 4633 67 12 79 55 1608 4489 10586 1320
		0,1222 697 696 985 29 12 #Pell(5,4) 41 17 696 841 2378 408	0,12221 1275 2668 2957 46 29 75 17 2668 2116 6900 986 #p2a	0,122211 1853 5796 6085 63 46 109 17 5796 3969 13734 1564
				0,122212 12525 11132 16757 121 46 167 75 11132 14641 40414 6900
				0,122213 9975 6032 11657 104 29 133 75 6032 10816 27664 4350
			0,12222 4059 4060 5741 70 29 #Pell(6,5) 99 41 4060 4900 13860 2378	0,122221 7421 15540 17221 111 70 181 41 15540 12321 40182 5740
				0,122222 23661 23660 33461 169 70 #Pell(7,6) 239 99 23660 28561 80782 13860
				0,122223 15543 7424 17225 128 29 157 99 7424 16384 40192 5742
			0,12223 2665 1272 2953 53 12 65 41 1272 2809 6890 984	0,122231 6027 9964 11645 94 53 147 41 9964 8836 27636 4346 #p3a
				0,122232 11115 12508 16733 118 53 171 65 12508 13924 40356 6890
				0,122233 5785 1848 6073 77 12 89 65 1848 5929 13706 1560
		0,1223 459 220 509 22 5 27 17 220 484 1188 170	0,12231 1037 1716 2005 39 22 61 17 1716 1521 4758 748	0,122311 1615 4368 4657 56 39 95 17 4368 3136 10640 1326
				0,122312 8479 7800 11521 100 39 139 61 7800 10000 27800 4758
				0,122313 6405 3652 7373 83 22 105 61 3652 6889 17430 2684
			0,12232 1917 2156 2885 49 22 71 27 2156 2401 6958 1188	0,122321 3375 7448 8177 76 49 125 27 7448 5776 19000 2646
				0,122322 11999 11760 16801 120 49 169 71 11760 14400 40560 6958
				0,122323 8165 4092 9133 93 22 115 71 4092 8649 21390 3124
			0,12233 999 320 1049 32 5 37 27 320 1024 2368 270	0,122331 2457 3776 4505 59 32 91 27 3776 3481 10738 1728
				0,122332 3737 4416 5785 69 32 101 37 4416 4761 13938 2368
				0,122333 1739 420 1789 42 5 47 37 420 1764 3948 370
	0,123 77 36 85 9 2 11 7 36 81 not coprime 198 28	0,1231 1,323 175 288 337 16 9 25 7 288 256 800 126	0,12311 273 736 785 23 16 39 7 736 529 1794 224	0,123111 371 1380 1429 30 23 53 7 1380 900 3180 322
				0,123112 3315 2852 4373 62 23 85 39 2852 3844 10540 1794
				0,123113 2769 1760 3281 55 16 71 39 1760 3025 7810 1248
			0,12312 1425 1312 1937 41 16 57 25 1312 1681 4674 800	0,123121 2675 5412 6037 66 41 107 25 5412 4356 14124 2050
				0,123122 7923 8036 11285 98 41 139 57 8036 9604 27244 4674
				0,123123 5073 2336 5585 73 16 89 57 2336 5329 12994 1824
			0,12313 1075 612 1237 34 9 43 25 612 1156 2924 450	0,123131 2325 4012 4637 59 34 93 25 4012 3481 10974 1700
				0,123132 4773 5236 7085 77 34 111 43 5236 5929 17094 2924
				0,123133 2623 936 2785 52 9 61 43 936 2704 6344 774
		0,1232 319 360 481 20 9 29 11 360 400 1160 198	0,12321 561 1240 1361 31 20 51 11 1240 961 3162 440	0,123211 803 2604 2725 42 31 73 11 2604 1764 6132 682
0,123212 5763 5084 7685 82 31 113 51 5084 6724 18532 3162
0,123213 4641 2840 5441 71 20 91 51 2840 5041 12922 2040
0,12322 2001 1960 2801 49 20 69 29 1960 2401 6762 1160			0,123221 3683 7644 8485 78 49 127 29 7644 6084 19812 2842
			0,123222 11523 11564 16325 118 49 167 69 11564 13924 39412 6762
			0,123223 7521 3560 8321 89 20 109 69 3560 7921 19402 2760
0,12323 1363 684 1525 38 9 47 29 684 1444 3572 522			0,123231 3045 5092 5933 67 38 105 29 5092 4489 14070 2204
			0,123232 5781 6460 8669 85 38 123 47 6460 7225 20910 3572
			0,123233 3055 1008 3217 56 9 65 47 1008 3136 7280 846
0,1233 1,1321 165 52 173 13 2 15 11 52 169 390 44		0,12331 407 624 745 24 13 37 11 624 576 1776 286	0,123311 649 1680 1801 35 24 59 11 1680 1225 4130 528
			0,123312 3145 2928 4297 61 24 85 37 2928 3721 10370 1776
			0,123313 2331 1300 2669 50 13 63 37 1300 2500 6300 962
		0,12332 615 728 953 28 13 41 15 728 784 2296 390	0,123321 1065 2408 2633 43 28 71 15 2408 1849 6106 840
			0,123322 3977 3864 5545 69 28 97 41 3864 4761 13386 2296
			0,123323 2747 1404 3085 54 13 67 41 1404 2916 7236 1066
		0,12333 285 68 293 17 2 19 15 68 289 646 60	0,123331 735 1088 1313 32 17 49 15 1088 1024 3136 510
			0,123332 1,11122 1007 1224 1585 36 17 53 19 1224 1296 3816 646
			0,123333 437 84 445 21 2 23 19 84 441n 966 76
0,13 1,2 15 8 17 4 1 #Pythagoras(2) 5 3 8 16 40 6	0,131 33 56 65 7 4 11 3 56 49 54 24	0,1311 51 140 149 10 7 17 3 140 100 340 42	0,13111 69 260 269 13 10 23 3 260 169 598 60	0,131111 87 416 425 16 13 29 3 416 256 928 78
				0,131112 1127 936 1465 36 13 49 23 936 1296 3528 598
				0,131113 989 660 1189 33 10 43 23 660 1089 2838 460
			0,13112 629 540 829 27 10 37 17 540 729 1998 340	0,131121 1,22123 1207 2376 2665 44 27 71 17 2376 1936 6248 918
				0,131122 3367 3456 4825 64 27 91 37 3456 4096 11648 1998
				0,131123 2109 940 2309 47 10 57 37 940 2209 5358 740
			0,13113 527 336 625 24 7 31 17 336 576 1488 238	0,131131 1105 1968 2257 41 24 65 17 1968 1681 5330 816
				0,131132 2449 2640 3601 55 24 79 31 2640 3025 8690 1488
				0,131133 1395 532 1493 38 7 45 31 532 1444 3420 434
		0,1312 275 252 373 18 7 25 11 252 324 900 154	0,13121 517 1044 1165 29 18 47 11 1044 841 2726 396	0,131211 759 2320 2441 40 29 69 11 2320 1600 5520 638
				0,131212 4935 4408 6617 76 29 105 47 4408 5776 15960 2726
				0,131213 3901 2340 4549 65 18 83 47 2340 4225 10790 1692
			0,13122 1525 1548 2173 43 18 61 25 1548 1849 5246 900	0,131221 2775 5848 6473 68 43 111 25 5848 4624 15096 2150
				0,131222 8967 8944 12665 104 43 147 61 8944 10816 30576 5246
				0,131223 5917 2844 6565 79 18 97 61 2844 6241 15326 2196
			0,13123 975 448 1073 32 7 39 25 448 1024 2496 350	0,131231 2225 3648 4273 57 32 89 25 3648 3249 10146 1600
				0,131232 4017 4544 6065 71 32 103 39 4544 5041 14626 2496
				0,131233 2067 644 2165 46 7 53 39 644 2116 4876 546
		0,1313 1,13211 209 120 241 15 4 19 11 120 225 570 88	0,13131 451 780 901 26 15 41 11 780 676 2132 330	0,131311 693 1924 2045 37 26 63 11 1924 1369 4662 572
				0,131312 3813 3484 5165 67 26 93 41 3484 4489 12462 2132
				0,131313 2911 1680 3361 56 15 71 41 1680 3136 7952 1230
			0,13132 931 1020 1381 34 15 49 19 1020 1156 3332 570	0,131321 1653 3604 3965 53 34 87 19 3604 2809 9222 1292
				0,131322 5733 5644 8045 83 34 117 49 5644 6889 19422 3332
				0,131323 3871 1920 4321 64 15 79 49 1920 4096 10112 1470
			0,13133 513 184 545 23 4 27 19 184 529 1242 152	0,131331 1235 1932 2293 42 23 65 19 1932 1764 5460 874
				0,131332 1971 2300 3029 50 23 73 27 2300 2500 7300 1242
				0,131333 945 248 977 31 4 35 27 248 961 2170 216
	0,132 65 72 97 9 4 13 5 72 81 234 40	0,1321 1,1213 115 252 277 14 9 23 5 252 196 644 90	0,13211 1,1231 165 532 557 19 14 33 5 532 361 1254 140	0,132111 1,1233 215 912 937 24 19 43 5 912 576 2064 190
				0,132112 2343 1976 3065 52 19 71 33 1976 2704 7384 1254
				0,132113 2013 1316 2405 47 14 61 33 1316 2209 5734 924
			0,13212 1173 1036 1565 37 14 51 23 1036 1369 3774 644	0,132121 2231 4440 4969 60 37 97 23 4440 3600 11640 1702
				0,132122 6375 6512 9113 88 37 125 51 6512 7744 22000 3774
				0,132123 4029 1820 4421 65 14 79 51 1820 4225 10270 1428
			0,13213 943 576 1105 32 9 41 23 576 1024 2624 414	0,132131 2001 3520 4049 55 32 87 23 3520 3025 9570 1472
				0,132132 4305 4672 6353 73 32 105 41 4672 5329 15330 2624
				0,132133 2419 900 2581 50 9 59 41 900 2500 5900 738
		0,1322 403 396 565 22 9 31 13 396 484 1364 234	0,13221 741 1540 1709 35 22 57 13 1540 1225 3990 572	0,132211 1,13223 1079 3360 3529 48 35 83 13 3360 2304 7968 910
				0,132212 7239 6440 9689 92 35 127 57 6440 8464 23368 3990
				0,132213 5757 3476 6725 79 22 101nbsp;57 3476 6241 15958 2508
			0,13222 2325 2332 3293 53 22 75 31 2332 2809 7950 1364	0,132221 4247 8904 9865 84 53 137 31 8904 7056 23016 3286
				0,132222 13575 13568 19193 128 53 181 75 13568 16384 46336 7950
				0,132223 8925 4268 9893 97 22 119 75 4268 9409 23086 3300
			0,13223 1,11232 1519 720 1681 40 9 49 31 720 1600 3920 558	0,132231 3441 5680 6641 71 40 111 31 5680 5041 15762 2480
				0,132232 6321 7120 9521 89 40 129 49 7120 7921 22962 3920
				0,132233 3283 1044 3445 58 9 67 49 1044 3364 7772 882
		0,1323 273 136 305 17 4 21 13 136 289 714 104	0,13231 611 1020 1189 30 17 47 13 1020 900 2820 442	0,132311 949 2580 2749 43 30 73 13 2580 1849 6278 780
				0,132312 5029 4620 6829 77 30 107 47 4620 5929 16478 2820
				0,132313 3807 2176 4385 64 17 81 47 2176 4096 10368 1598
			0,13232 1155 1292 1733 38 17 55 21 1292 1444 4180 714	0,132321 2037 4484 4925 59 38 97 21 4484 3481 11446 1596
				0,132322 7205 7068 10093 93 38 131 55 7068 8649 24366 4180
				0,132323 4895 2448 5473 72 17 89 55 2448 5184 12816 1870
			0,13233 609 200 641 25 4 29 21 200 625 1450 168	0,132331 1491 2300 2741 46 25 71 21 2300 2116 6532 1050
				0,132332 2291 2700 3541 54 25 79 29 2700 2916 8532 1450
				0,132333 1073 264 1105 33 4 37 29 264 1089 2442 232
	0,133 35 12 37 6 1 #Pythagoras(3) 7 5 12 36 84 10	0,1331 85 132 157 11 6 17 5 132 121 374 60	0,13311 1,223 135 352 377 16 11 27 5 352 256 864 110	0,133111 185 672 697 21 16 37 5 672 441 1554 160
				0,133112 1593 1376 2105 43 16 59 27 1376 1849 5074 864
				0,133113 1323 836 1565 38 11 49 27 836 1444 3724 594
			0,13312 663 616 905 28 11 39 17 616 784 2184 374	0,133121 1241 2520 2809 45 28 73 17 2520 2025 6570 952
				0,133122 3705 3752 5273 67 28 95 39 3752 4489 12730 2184
				0,133123 2379 1100 2621 50 11 61 39 1100 2500 6100 858
			0,13313 493 276 565 23 6 b n 29 17 276 529 1334 204	0,133131 1,21323 1071 1840 2129 40 23 63 17 1840 1600 5040 782
				0,133132 1,23122 2175 2392 3233 52 23 75 29 2392 2704 7800 1334
				0,133133 1,23321 1189 420 1261 35 6 41 29 420 1225 2870 348
		0,1332 1,2121 133 156 205 13 6 19 7 156 169 494 84	0,13321 231 520 569 20 13 33 7 520 400 1320 182	0,133211 329 1080 1129 27 20 47 7 1080 729 2538 280
0,133212 2409 2120 3209 53 20 73 33 2120 2809 7738 1320
0,133213 1947 1196 2285 46 13 59 33 1196 2116 5428 858
0,13322 855 832 1193 32 13 45 19 832 1024 2880 494			0,133221 1577 3264 3625 51 32 83 19 3264 2601 8466 1216
			0,133222 4905 4928 6953 77 32 109 45 4928 5929 16786 2880
			0,133223 3195 1508 3533 58 13 71 45 1508 3364 8236 1170
0,13323 589 300 661 25 6 31 19 300 625 1550 228			0,133231 1311 2200 2561 44 25 69 19 2200 1936 6072 950
			0,133232 2511 2800 3761 56 25 81 31 2800 3136 9072 1550
			0,133233 1333 444 1405 37 6 43 31 444 1369 3182 372
0,1333 63 16 65 8 1 #Pythagoras(4) 9 7 16 64 144 14		0,13331 1,32111 161 240 289 15 8 23 7 240 225 690 112	0,133311 259 660 709 22 15 37 7 660 484 1628 210
			0,133312 1219 1140 1669 38 15 53 23 1140 1444 4028 690
			0,133313 897 496 1025 31 8 39 23 496 961 2418 368
		0,13332 225 272 353 17 8 25 9 272 289 850 144	0,133321 387 884 965 26 17 43 9 884 676 2236 306
			0,133322 1475 1428 2053 42 17 59 25 1428 1764 4956 850
			0,133323 1025 528 1153 33 8 41 25 528 1089 2706 400
		0,13333 99 20 101 10 1 #Pythagoras(5) 11 9 20 100 220 18	0,133331 261 380 461 19 10 29 9 380 361 1102 180
			0,133332 341 420 541 21 10 31 11 420 441 1302 220
			0,133333 1,132 143 24 145 12 1 #Pythagoras(6) 13 11 24 144 312 22
top of table

Notes: added some (u, v) pairs ; intermittent saving regards Gangleri 16:32, 13 July 2019 (UTC)

details to Berggrens's tree

to be continued 2A02:810D:41C0:134:6C5D:2ACF:DA6:D533 (talk) 18:07, 12 July 2019 (UTC)

sorted (b, n) pairs for the Berggrens's tree regards

4 4 12 9 24 16 40 25 60 36 84 49 204 289 160 256 140 196 644 529 924 1089 240 576 104 169 572 484 780 900 168 441 88 121 396 324 900 625 1692 2209 880 1600 572 676 2132 1681 3276 3969 1056 2304 152 361 1292 1156 1596 1764 216 729 60 100 340 289 816 576 1496 1936 740 1369 460 529 1656 1296 2576 3136 860 1849 96 256 928 841 1120 1225 132 484 48 64 208 169 468 324 828 529 1764 2401 1144 1936 884 1156 3740 3025 5508 6561 1560 3600 464 841 2900 2500 3828 4356 720 2025 304 361 1140 900 2460 1681 4740 6241 2584 4624 1748 2116 6716 5329 10212 12321 3192 7056 560 1225 4340 3844 5460 6084 816 2601 84 196 700 625 1800 1296 3200 4096 1484 2809 868 961 2976 2304 4712 5776 1652 3481 120 400 1480 1369 1720 1849 156 676 28 49 168 144 408 289 748 484 1564 2116 984 1681 744 961 3100 2500 4588 5476 1320 3025 364 676 2340 2025 3068 3481 560 1600 224 256 800 625 1700 1156 3300 4356 1824 3249 1248 1521 4836 3844 7332 8836 2272 5041 420 900 3180 2809 4020 4489 616 1936 44 121 440 400 1160 841 2040 2601 924 1764 528 576 1776 1369 2832 3481 1012 2116 60 225 840 784 960 1024 76 361 20 25 80 64 176 121 308 196 476 289 1092 1521 792 1296 660 900 2940 2401 4260 5041 1144 2704 432 729 2484 2116 3348 3844 688 1849 336 441 1428 1156 3196 2209 6052 7921 3192 5776 2100 2500 7900 6241 12100 14641 3864 8464 592 1369 4884 4356 6068 6724 848 2809 180 324 1116 961 2728 1936 4960 6400 2412 4489 1476 1681 5248 4096 8200 10000 2772 5929 280 784 2856 2601 3416 3721 380 1444 120 144 456 361 988 676 1716 1089 3692 5041 2432 4096 1900 2500 8100 6561 11900 14161 3344 7744 1032 1849 6364 5476 8428 9604 1608 4489 696 841 2668 2116 5796 3969 11132 14641 6032 10816 4060 4900 15540 12321 23660 28561 7424 16384 1272 2809 9964 8836 12508 13924 1848 5929 220 484 1716 1521 4368 3136 7800 10000 3652 6889 2156 2401 7448 5776 11760 14400 4092 8649 320 1024 3776 3481 4416 4761 420 1764 36 81 288 256 736 529 1380 900 2852 3844 1760 3025 1312 1681 5412 4356 8036 9604 2336 5329 612 1156 4012 3481 5236 5929 936 2704 360 400 1240 961 2604 1764 5084 6724 2840 5041 1960 2401 7644 6084 11564 13924 3560 7921 684 1444 5092 4489 6460 7225 1008 3136 52 169 624 576 1680 1225 2928 3721 1300 2500 728 784 2408 1849 3864 4761 1404 2916 68 289 1088 1024 1224 1296 84 441 8 16 56 49 140 100 260 169 416 256 936 1296 660 1089 540 729 2376 1936 3456 4096 940 2209 336 576 1968 1681 2640 3025 532 1444 252 324 1044 841 2320 1600 4408 5776 2340 4225 1548 1849 5848 4624 8944 10816 2844 6241 448 1024 3648 3249 4544 5041 644 2116 120 225 780 676 1924 1369 3484 4489 1680 3136 1020 1156 3604 2809 5644 6889 1920 4096 184 529 1932 1764 2300 2500 248 961 72 81 252 196 532 361 912 576 1976 2704 1316 2209 1036 1369 4440 3600 6512 7744 1820 4225 576 1024 3520 3025 4672 5329 900 2500 396 484 1540 1225 3360 2304 6440 8464 3476 6241 2332 2809 8904 7056 13568 16384 4268 9409 720 1600 5680 5041 7120 7921 1044 3364 136 289 1020 900 2580 1849 4620 5929 2176 4096 1292 1444 4484 3481 7068 8649 2448 5184 200 625 2300 2116 2700 2916 264 1089 12 36 132 121 352 256 672 441 1376 1849 836 1444 616 784 2520 2025 3752 4489 1100 2500 276 529 1840 1600 2392 2704 420 1225 156 169 520 400 1080 729 2120 2809 1196 2116 832 1024 3264 2601 4928 5929 1508 3364 300 625 2200 1936 2800 3136 444 1369 16 64 240 225 660 484 1140 1444 496 961 272 289 884 676 1428 1764 528 1089 20 100 380 361 420 441 24 144

added sorted (b, n) pairs for the Berggrens's tree; regards Gangleri 217.86.249.144 (talk) 13:14, 16 July 2019 (UTC)

---

triplets contained in both trees

1_0_1|0 1 0 1 1_0_1|0 1 0 1 1 1005_2132_2357|0,111221 1005 2132 2357 1005_2132_2357|1,31221 1005 2132 2357 1 1007_1224_1585|0,123332 1007 1224 1585 1007_1224_1585|1,11122 1007 1224 1585 1 101_5100_5101|1,31131 101 5100 5101 1015_192_1033|1,2332 1015 192 1033 10205_10212_14437|0,112222 10205 10212 14437 1023_64_1025|1,3332 1023 64 1025 1025_528_1153|0,133323 1025 528 1153 103_5304_5305|1,31133 103 5304 5305 1037_1716_2005|0,12231 1037 1716 2005 1045_4452_4573|1,22231 1045 4452 4573 105_208_233|0,1121 105 208 233 105_208_233|1,12111 105 208 233 1 105_5512_5513|1,31311 105 5512 5513 105_608_617|1,21111 105 608 617 105_88_137|0,1112 105 88 137 105_88_137|1,3211 105 88 137 1 1053_3196_3365|0,121211 1053 3196 3365 1065_2408_2633|0,123321 1065 2408 2633 107_5724_5725|1,31313 107 5724 5725 1071_1840_2129|0,133131 1071 1840 2129 1071_1840_2129|1,21323 1071 1840 2129 1 1071_7040_7121|1,32233 1071 7040 7121 1073_264_1105|0,132333 1073 264 1105 1075_612_1237|0,12313 1075 612 1237 1079_3360_3529|0,132211 1079 3360 3529 1079_3360_3529|1,13223 1079 3360 3529 1 1085_132_1093|1,33321 1085 132 1093 109_5940_5941|1,31331 109 5940 5941 11_60_61|0,11111 11 60 61 11_60_61|1,13 11 60 61 1 1105_1968_2257|0,131131 1105 1968 2257 1107_476_1205|1,12212 1107 476 1205 111_6160_6161|1,31333 111 6160 6161 111_680_689|1,2133 111 680 689 11115_12508_16733|0,122232 11115 12508 16733 1127_936_1465|0,131112 1127 936 1465 113_6384_6385|1,33111 113 6384 6385 1131_340_1181|1,22112 1131 340 1181 1147_204_1165|1,21312 1147 204 1165 115_252_277|0,1321 115 252 277 115_252_277|1,1213 115 252 277 1 115_6612_6613|1,33113 115 6612 6613 11523_11564_16325|0,123222 11523 11564 16325 1155_1292_1733|0,13232 1155 1292 1733 1155_68_1157|1,11112 1155 68 1157 1157_3876_4045|1,23231 1157 3876 4045 1159_1680_2041|1,11323 1159 1680 2041 1161_560_1289|0,11223 1161 560 1289 11661_11900_16661|0,122122 11661 11900 16661 117_44_125|0,1133 117 44 125 117_44_125|1,1121 117 44 125 1 117_6844_6845|1,33131 117 6844 6845 1173_1036_1565|0,13212 1173 1036 1565 1175_792_1417|0,121113 1175 792 1417 1175_792_1417|1,32122 1175 792 1417 1 1189_420_1261|0,133133 1189 420 1261 1189_420_1261|1,23321 1189 420 1261 1 119_120_169|0,122 119 120 169 119_120_169|1,122 119 120 169 1 119_7080_7081|1,33133 119 7080 7081 11999_11760_16801|0,122322 11999 11760 16801 1207_2376_2665|0,131121 1207 2376 2665 1207_2376_2665|1,22123 1207 2376 2665 1 121_7320_7321|1,33311 121 7320 7321 12141_12100_17141|0,121222 12141 12100 17141 1219_1140_1669|0,133312 1219 1140 1669 123_7564_7565|1,33313 123 7564 7565 123_836_845|1,21113 123 836 845 1235_1932_2293|0,131331 1235 1932 2293 1239_1520_1961|1,11322 1239 1520 1961 1241_2520_2809|0,133121 1241 2520 2809 1245_3332_3557|1,33231 1245 3332 3557 1247_504_1345|1,32132 1247 504 1345 125_7812_7813|1,33331 125 7812 7813 12525_11132_16757|0,122212 12525 11132 16757 1265_1248_1777|0,11322 1265 1248 1777 1269_740_1469|0,111313 1269 740 1469 1269_740_1469|1,22321 1269 740 1469 1 127_8064_8065|1,33333 127 8064 8065 1275_2668_2957|0,12221 1275 2668 2957 1275_988_1613|1,23212 1275 988 1613 1287_4816_4985|1,31233 1287 4816 4985 1287_6784_6905|1,22233 1287 6784 6905 129_920_929|1,2311 129 920 929 1295_72_1297|1,11132 1295 72 1297 13_84_85|0,111111 13 84 85 13_84_85|1,31 13 84 85 1 1305_592_1433|0,12123 1305 592 1433 1309_2820_3109|1,33221 1309 2820 3109 1311_1360_1889|1,21322 1311 1360 1889 1311_2200_2561|0,133231 1311 2200 2561 1323_836_1565|0,133113 1323 836 1565 1325_1092_1717|0,121112 1325 1092 1717 1325_1092_1717|1,32321 1325 1092 1717 1 133_156_205|0,1332 133 156 205 133_156_205|1,2121 133 156 205 1 1333_444_1405|0,133233 1333 444 1405 1343_2976_3265|0,112321 1343 2976 3265 1343_2976_3265|1,12223 1343 2976 3265 1 1349_2340_2701|0,113131 1349 2340 2701 1349_2340_2701|1,23221 1349 2340 2701 1 135_352_377|0,13311 135 352 377 135_352_377|1,223 135 352 377 1 1357_1476_2005|0,12132 1357 1476 2005 1357_1476_2005|1,32221 1357 1476 2005 1 13575_13568_19193|0,132222 13575 13568 19193 1363_684_1525|0,12323 1363 684 1525 1365_1892_2333|1,22221 1365 1892 2333 1387_2484_2845|0,121131 1387 2484 2845 1395_532_1493|0,131133 1395 532 1493 1403_1596_2125|0,111232 1403 1596 2125 1407_2024_2465|1,13123 1407 2024 2465 141_1100_1109|1,21131 141 1100 1109 1419_380_1469|0,121333 1419 380 1469 1419_380_1469|1,12312 1419 380 1469 1 1425_1312_1937|0,12312 1425 1312 1937 143_24_145|0,133333 143 24 145 143_24_145|1,132 143 24 145 1 1431_1040_1769|1,21222 1431 1040 1769 1443_76_1445|1,11312 1443 76 1445 1449_1720_2249|0,112332 1449 1720 2249 145_408_433|0,11311 145 408 433 145_408_433|1,2211 145 408 433 1 1455_4592_4817|1,31223 1455 4592 4817 1463_2784_3145|1,12323 1463 2784 3145 147_1196_1205|1,2313 147 1196 1205 1475_1428_2053|0,133322 1475 1428 2053 1479_880_1721|0,111213 1479 880 1721 1479_880_1721|1,11222 1479 880 1721 1 1491_2300_2741|0,132331 1491 2300 2741 1495_1848_2377|1,13122 1495 1848 2377 1495_6528_6697|1,23233 1495 6528 6697 15_112_113|1,33 15 112 113 15_8_17|0,13 15 8 17 15_8_17|1,2 15 8 17 1 1501_2940_3301|0,121121 1501 2940 3301 1519_720_1681|0,13223 1519 720 1681 1519_720_1681|1,11232 1519 720 1681 1 1525_1548_2173|0,13122 1525 1548 2173 153_104_185|0,11113 153 104 185 153_104_185|1,11211 153 104 185 1 1537_984_1825|0,113113 1537 984 1825 1539_3100_3461|0,113121 1539 3100 3461 155_468_493|0,11211 155 468 493 155_468_493|1,12113 155 468 493 1 1551_560_1649|0,113133 1551 560 1649 1551_560_1649|1,21232 1551 560 1649 1 15543_7424_17225|0,122223 15543 7424 17225 1577_3264_3625|0,133221 1577 3264 3625 159_1400_1409|1,21133 159 1400 1409 1591_240_1609|1,21332 1591 240 1609 1593_1376_2105|0,133112 1593 1376 2105 1599_80_1601|1,11332 1599 80 1601 161_240_289|0,13331 161 240 289 161_240_289|1,32111 161 240 289 1 1615_4368_4657|0,122311 1615 4368 4657 1643_924_1885|0,113313 1643 924 1885 1643_924_1885|1,22212 1643 924 1885 1 1647_1496_2225|0,111312 1647 1496 2225 1647_1496_2225|1,22122 1647 1496 2225 1 165_1508_1517|1,2331 165 1508 1517 165_52_173|0,1233 165 52 173 165_52_173|1,1321 165 52 173 1 165_532_557|0,13211 165 532 557 165_532_557|1,1231 165 532 557 1 1653_3604_3965|0,131321 1653 3604 3965 1659_2900_3341|0,112131 1659 2900 3341 1679_2400_2929|1,13323 1679 2400 2929 1695_6272_6497|1,33233 1695 6272 6497 17_144_145|1,111 17 144 145 1705_1032_1993|0,12213 1705 1032 1993 171_140_221|0,11112 171 140 221 171_140_221|1,1212 171 140 221 1 1739_420_1789|0,122333 1739 420 1789 1749_860_1949|0,111323 1749 860 1949 175_288_337|0,1231 175 288 337 175_288_337|1,323 175 288 337 1 1755_1748_2477|0,11222 1755 1748 2477 1763_84_1765|1,13112 1763 84 1765 1767_1144_2105|0,112113 1767 1144 2105 177_1736_1745|1,21311 177 1736 1745 1775_2208_2833|1,13322 1775 2208 2833 1785_688_1913|0,121133 1785 688 1913 1817_2856_3385|0,121331 1817 2856 3385 1827_1564_2405|0,113112 1827 1564 2405 183_1856_1865|1,2333 183 1856 1865 185_672_697|0,133111 185 672 697 1853_5796_6085|0,122211 1853 5796 6085 1863_3016_3545|1,23123 1863 3016 3545 1869_3740_4181|0,112121 1869 3740 4181 187_84_205|0,1123 187 84 205 187_84_205|1,2112 187 84 205 1 1885_1692_2533|0,111212 1885 1692 2533 1887_6016_6305|1,33223 1887 6016 6305 1887_616_1985|0,113233 1887 616 1985 189_340_389|0,11131 189 340 389 189_340_389|1,1221 189 340 389 1 19_180_181|1,113 19 180 181 1909_3180_3709|0,113231 1909 3180 3709 1911_440_1961|1,22132 1911 440 1961 1917_2156_2885|0,12232 1917 2156 2885 1935_88_1937|1,13132 1935 88 1937 1943_1824_2665|1,12322 1943 1824 2665 1947_1196_2285|0,133213 1947 1196 2285 195_2108_2117|1,21313 195 2108 2117 195_28_197|1,312 195 28 197 195_748_773|0,113111 195 748 773 195_748_773|1,2213 195 748 773 1 1961_720_2089|0,112133 1961 720 2089 1971_2300_3029|0,131332 1971 2300 3029 1975_2808_3433|1,31123 1975 2808 3433 1995_1012_2237|0,113323 1995 1012 2237 2001_1960_2801|0,12322 2001 1960 2801 2001_3520_4049|0,132131 2001 3520 4049 2013_1316_2405|0,132113 2013 1316 2405 2015_1632_2593|1,12222 2015 1632 2593 203_396_445|0,11121 203 396 445 203_396_445|1,3213 203 396 445 1 2035_828_2197|1,32212 2035 828 2197 2037_4484_4925|0,132321 2037 4484 4925 205_828_853|0,112111 205 828 853 205_828_853|1,12131 205 828 853 1 2059_2100_2941|0,12122 2059 2100 2941 2067_644_2165|0,131233 2067 644 2165 207_224_305|0,1132 207 224 305 207_224_305|1,322 207 224 305 1 2071_5760_6121|1,23223 2071 5760 6121 2077_1764_2725|0,112112 2077 1764 2725 2079_2600_3329|1,31122 2079 2600 3329 209_120_241|0,1313 209 120 241 209_120_241|1,13211 209 120 241 1 21_20_29|0,12 21 20 29 21_20_29|1,21 21 20 29 1 21_220_221|1,131 21 220 221 2107_276_2125|1,23112 2107 276 2125 2109_940_2309|0,131123 2109 940 2309 2115_92_2117|1,13312 2115 92 2117 213_2516_2525|1,21331 213 2516 2525 2135_1248_2473|1,13222 2135 1248 2473 2139_1900_2861|0,12212 2139 1900 2861 215_912_937|0,132111 215 912 937 215_912_937|1,1233 215 912 937 1 217_456_505|0,1221 217 456 505 217_456_505|1,21211 217 456 505 1 2175_2392_3233|0,133132 2175 2392 3233 2175_2392_3233|1,23122 2175 2392 3233 1 2183_1056_2425|0,111223 2183 1056 2425 2183_1056_2425|1,13232 2183 1056 2425 1 2201_2040_3001|0,113312 2201 2040 3001 221_60_229|0,11333 221 60 229 221_60_229|1,3121 221 60 229 1 2225_3648_4273|0,131231 2225 3648 4273 2231_4440_4969|0,132121 2231 4440 4969 2247_5504_5945|1,22223 2247 5504 5945 225_272_353|0,13332 225 272 353 2255_672_2353|1,12232 2255 672 2353 2279_480_2329|1,12332 2279 480 2329 2291_2700_3541|0,132332 2291 2700 3541 2295_3248_3977|1,31323 2295 3248 3977 23_264_265|1,133 23 264 265 2303_96_2305|1,13332 2303 96 2305 231_160_281|0,111113 231 160 281 231_160_281|1,222 231 160 281 1 231_2960_2969|1,21333 231 2960 2969 231_520_569|0,13321 231 520 569 231_520_569|1,2123 231 520 569 1 2323_4836_5365|0,113221 2323 4836 5365 2325_2332_3293|0,13222 2325 2332 3293 2325_4012_4637|0,123131 2325 4012 4637 2331_1300_2669|0,123313 2331 1300 2669 2343_1976_3065|0,132112 2343 1976 3065 23661_23660_33461|0,122222 23661 23660 33461 2379_1100_2621|0,133123 2379 1100 2621 2407_3024_3865|1,31322 2407 3024 3865 2409_2120_3209|0,133212 2409 2120 3209 2415_5248_5777|0,121321 2415 5248 5777 2415_5248_5777|1,32223 2415 5248 5777 1 2419_900_2581|0,132133 2419 900 2581 2449_2640_3601|0,131132 2449 2640 3601 245_1188_1213|1,2231 245 1188 1213 2451_700_2549|1,32312 2451 700 2549 2457_3776_4505|0,122331 2457 3776 4505 247_96_265|0,11133 247 96 265 247_96_265|1,232 247 96 265 1 249_3440_3449|1,23111 249 3440 3449 2499_100_2501|1,31112 2499 100 2501 25_312_313|1,311 25 312 313 2511_2800_3761|0,133232 2511 2800 3761 253_204_325|0,111112 253 204 325 253_204_325|1,21121 253 204 325 1 2537_816_2665|0,112233 2537 816 2665 255_1288_1313|1,12133 255 1288 1313 255_32_257|1,332 255 32 257 2575_4992_5617|1,32323 2575 4992 5617 2583_1144_2825|0,121123 2583 1144 2825 259_660_709|0,133311 259 660 709 259_660_709|1,32113 259 660 709 1 2607_2576_3665|0,111322 2607 2576 3665 261_380_461|0,133331 261 380 461 261_380_461|1,12121 261 380 461 1 2613_1484_3005|0,112313 2613 1484 3005 2619_4340_5069|0,112231 2619 4340 5069 2623_936_2785|0,123133 2623 936 2785 2639_3720_4561|1,33123 2639 3720 4561 265_1392_1417|1,22111 265 1392 1417 2665_1272_2953|0,12223 2665 1272 2953 267_3956_3965|1,23113 267 3956 3965 2675_5412_6037|0,123121 2675 5412 6037 2695_312_2713|1,23132 2695 312 2713 27_364_365|1,313 27 364 365 2703_104_2705|1,31132 2703 104 2705 2727_4736_5465|1,22323 2727 4736 5465 273_136_305|0,1323 273 136 305 273_136_305|1,31211 273 136 305 1 273_736_785|0,12311 273 736 785 2745_848_2873|0,121233 2745 848 2873 2747_1404_3085|0,123323 2747 1404 3085 275_252_373|0,1312 275 252 373 275_252_373|1,3212 275 252 373 1 2759_3480_4441|1,33122 2759 3480 4441 2769_1760_3281|0,123113 2769 1760 3281 2775_5848_6473|0,131221 2775 5848 6473 279_440_521|0,11331 279 440 521 279_440_521|1,1123 279 440 521 1 2805_3068_4157|0,113132 2805 3068 4157 285_4508_4517|1,23131 285 4508 4517 285_68_293|0,12333 285 68 293 285_68_293|1,3321 285 68 293 1 287_816_865|0,111311 287 816 865 287_816_865|1,1223 287 816 865 1 2871_4480_5321|1,23323 2871 4480 5321 2881_1320_3169|0,113123 2881 1320 3169 2891_540_2941|1,22312 2891 540 2941 29_420_421|1,331 29 420 421 2905_2832_4057|0,113322 2905 2832 4057 2911_1680_3361|0,131313 2911 1680 3361 2911_1680_3361|1,31222 2911 1680 3361 1 2915_108_2917|1,31312 2915 108 2917 2937_3416_4505|0,121332 2937 3416 4505 295_1728_1753|1,2233 295 1728 1753 2967_1456_3305|1,31232 2967 1456 3305 297_304_425|0,1122 297 304 425 2987_4884_5725|0,121231 2987 4884 5725 299_180_349|0,1213 299 180 349 299_180_349|1,12112 299 180 349 1 2993_1824_3505|0,113213 2993 1824 3505 3_4_5|0,1 3 4 5 3_4_5|1 3 4 5 1 3007_4224_5185|1,33323 3007 4224 5185 301_900_949|0,111211 301 900 949 301_900_949|1,3231 301 900 949 1 303_5096_5105|1,23133 303 5096 5105 3045_5092_5933|0,123231 3045 5092 5933 305_1848_1873|1,12311 305 1848 1873 3055_1008_3217|0,123233 3055 1008 3217 31_480_481|1,333 31 480 481 3115_3348_4573|0,121132 3115 3348 4573 3135_112_3137|1,31332 3135 112 3137 3135_3968_5057|1,33322 3135 3968 5057 3145_2928_4297|0,123312 3145 2928 4297 315_1972_1997|1,22113 315 1972 1997 315_572_653|0,111131 315 572 653 315_572_653|1,11213 315 572 653 1 315_988_1037|0,12211 315 988 1037 315_988_1037|1,21213 315 988 1037 1 319_360_481|0,1232 319 360 481 319_360_481|1,1122 319 360 481 1 3195_1508_3533|0,133223 3195 1508 3533 321_5720_5729|1,23311 321 5720 5729 3213_6716_7445|0,112221 3213 6716 7445 323_36_325|1,1112 323 36 325 325_228_397|1,2321 325 228 397 3255_3712_4937|1,23322 3255 3712 4937 3283_1044_3445|0,132233 3283 1044 3445 3285_1652_3677|0,112323 3285 1652 3677 329_1080_1129|0,133211 329 1080 1129 329_1080_1129|1,12211 329 1080 1129 1 3293_3276_4645|0,111222 3293 3276 4645 33_544_545|1,1111 33 544 545 33_56_65|0,131 33 56 65 33_56_65|1,211 33 56 65 1 3315_2852_4373|0,123112 3315 2852 4373 333_644_725|0,111121 333 644 725 333_644_725|1,3221 333 644 725 1 3355_348_3373|1,23312 3355 348 3373 3363_116_3365|1,33112 3363 116 3365 3367_3456_4825|0,131122 3367 3456 4825 3367_3456_4825|1,22322 3367 3456 4825 1 3375_7448_8177|0,122321 3375 7448 8177 339_6380_6389|1,23313 339 6380 6389 341_420_541|0,133332 341 420 541 341_420_541|1,2221 341 420 541 1 3431_1560_3769|0,112123 3431 1560 3769 3441_5680_6641|0,132231 3441 5680 6641 345_152_377|0,11123 345 152 377 345_152_377|1,33211 345 152 377 1 3471_3200_4721|0,112312 3471 3200 4721 3471_3200_4721|1,32322 3471 3200 4721 1 35_12_37|0,133 35 12 37 35_12_37|1,12 35 12 37 1 35_612_613|1,1113 35 612 613 351_280_449|1,2122 351 280 449 3515_3828_5197|0,112132 3515 3828 5197 355_2508_2533|1,12313 355 2508 2533 3567_2944_4625|1,32222 3567 2944 4625 357_1276_1325|1,32131 357 1276 1325 357_7076_7085|1,23331 357 7076 7085 357_76_365|0,113333 357 76 365 357_76_365|1,11121 357 76 365 1 3589_4020_5389|0,113232 3589 4020 5389 3599_120_3601|1,33132 3599 120 3601 3627_6364_7325|0,122131 3627 6364 7325 365_2652_2677|1,22131 365 2652 2677 3655_2688_4537|1,22222 3655 2688 4537 3683_7644_8485|0,123221 3683 7644 8485 369_800_881|0,11321 369 800 881 37_684_685|1,1131 37 684 685 3705_3752_5273|0,133122 3705 3752 5273 371_1380_1429|0,123111 371 1380 1429 3731_3300_4981|0,113212 3731 3300 4981 3735_2432_4457|0,122113 3735 2432 4457 3735_2432_4457|1,23222 3735 2432 4457 1 3737_4416_5785|0,122332 3737 4416 5785 3741_7900_8741|0,121221 3741 7900 8741 375_7808_7817|1,23333 375 7808 7817 377_336_505|0,1212 377 336 505 3807_2176_4385|0,132313 3807 2176 4385 3807_2176_4385|1,33222 3807 2176 4385 1 3813_3484_5165|0,131312 3813 3484 5165 3843_124_3845|1,33312 3843 124 3845 387_884_965|0,133321 387 884 965 3871_1920_4321|0,131323 3871 1920 4321 3871_1920_4321|1,33232 3871 1920 4321 1 39_760_761|1,1133 39 760 761 39_80_89|0,121 39 80 89 39_80_89|1,23 39 80 89 1 3901_2340_4549|0,131213 3901 2340 4549 391_120_409|0,11233 391 120 409 391_120_409|1,2132 391 120 409 1 3927_1664_4265|1,23232 3927 1664 4265 3975_1408_4217|1,22232 3975 1408 4217 3977_3864_5545|0,123322 3977 3864 5545 399_1600_1649|1,3233 399 1600 1649 399_40_401|1,1132 399 40 401 4015_1152_4177|1,32232 4015 1152 4177 4017_4544_6065|0,131232 4017 4544 6065 4029_1820_4421|0,132123 4029 1820 4421 403_396_565|0,1322 403 396 565 403_396_565|1,11212 403 396 565 1 4047_896_4145|1,32332 4047 896 4145 405_3268_3293|1,12331 405 3268 3293 4059_4060_5741|0,12222 4059 4060 5741 4061_8100_9061|0,122121 4061 8100 9061 407_624_745|0,12331 407 624 745 407_624_745|1,1323 407 624 745 1 4071_640_4121|1,22332 4071 640 4121 4087_384_4105|1,23332 4087 384 4105 4095_128_4097|1,33332 4095 128 4097 41_840_841|1,1311 41 840 841 413_1716_1765|0,122111 413 1716 1765 413_1716_1765|1,21231 413 1716 1765 1 4141_4260_5941|0,121122 4141 4260 5941 415_3432_3457|1,22133 415 3432 3457 4165_2412_4813|0,121313 4165 2412 4813 423_1064_1145|1,12123 423 1064 1145 4247_8904_9865|0,132221 4247 8904 9865 425_168_457|0,111133 425 168 457 4263_2584_4985|0,112213 4263 2584 4985 427_1836_1885|1,12213 427 1836 1885 429_460_629|0,11132 429 460 629 429_700_821|0,11231 429 700 821 429_700_821|1,32121 429 700 821 1 43_924_925|1,1313 43 924 925 4305_4672_6353|0,132132 4305 4672 6353 4345_1608_4633|0,122133 4345 1608 4633 435_308_533|1,32112 435 308 533 4365_3692_5717|0,122112 4365 3692 5717 437_84_445|0,123333 437 84 445 437_84_445|1,11321 437 84 445 1 441_1160_1241|0,113311 441 1160 1241 45_1012_1013|1,1331 45 1012 1013 45_28_53|0,113 45 28 53 45_28_53|1,121 45 28 53 1 451_780_901|0,13131 451 780 901 451_780_901|1,13213 451 780 901 1 4515_4588_6437|0,113122 4515 4588 6437 455_2088_2137|1,32133 455 2088 2137 455_4128_4153|1,12333 455 4128 4153 455_528_697|0,11332 455 528 697 455_528_697|1,1322 455 528 697 1 459_220_509|0,1223 459 220 509 459_220_509|1,2212 459 220 509 1 4641_2840_5441|0,123213 4641 2840 5441 465_4312_4337|1,22311 465 4312 4337 47_1104_1105|1,1333 47 1104 1105 475_132_493|0,111333 475 132 493 475_132_493|1,21112 475 132 493 1 477_1364_1445|1,11231 477 1364 1445 4773_5236_7085|0,123132 4773 5236 7085 4785_2272_5297|0,113223 4785 2272 5297 481_600_769|1,23211 481 600 769 4815_4712_6737|0,112322 4815 4712 6737 483_44_485|1,1312 483 44 485 4859_5460_7309|0,112232 4859 5460 7309 4895_2448_5473|0,132323 4895 2448 5473 49_1200_1201|1,3111 49 1200 1201 4905_4928_6953|0,133222 4905 4928 6953 493_276_565|0,13313 493 276 565 493_276_565|1,21321 493 276 565 1 4935_4408_6617|0,131212 4935 4408 6617 495_1472_1553|1,3223 495 1472 1553 495_952_1073|1,21123 495 952 1073 5_12_13|0,11 5 12 13 5_12_13|1,1 5 12 13 1 5029_4620_6829|0,132312 5029 4620 6829 5073_2336_5585|0,123123 5073 2336 5585 51_1300_1301|1,3113 51 1300 1301 51_140_149|0,1311 51 140 149 51_140_149|1,213 51 140 149 1 511_2640_2689|1,21233 511 2640 2689 513_184_545|0,13133 513 184 545 515_5292_5317|1,22313 515 5292 5317 517_1044_1165|0,13121 517 1044 1165 517_1044_1165|1,11221 517 1044 1165 1 525_2788_2837|1,12231 525 2788 2837 525_92_533|1,13121 525 92 533 527_336_625|0,13113 527 336 625 527_336_625|1,1222 527 336 625 1 53_1404_1405|1,3131 53 1404 1405 531_1700_1781|0,113211 531 1700 1781 533_756_925|1,21221 533 756 925 5335_3192_6217|0,121213 5335 3192 6217 5341_4740_7141|0,112212 5341 4740 7141 5355_6068_8093|0,121232 5355 6068 8093 539_1140_1261|0,11221 539 1140 1261 5405_5508_7717|0,112122 5405 5508 7717 5439_4960_7361|0,121312 5439 4960 7361 55_1512_1513|1,3133 55 1512 1513 55_48_73|0,112 55 48 73 55_48_73|1,22 55 48 73 1 551_240_601|0,111123 551 240 601 551_240_601|1,1232 551 240 601 1 553_3096_3145|1,32311 553 3096 3145 555_572_797|0,11122 555 572 797 555_572_797|1,13212 555 572 797 1 559_840_1009|0,113331 559 840 1009 559_840_1009|1,3123 559 840 1009 1 5605_2772_6253|0,121323 5605 2772 6253 561_1240_1361|0,12321 561 1240 1361 561_1240_1361|1,22211 561 1240 1361 1 565_6372_6397|1,22331 565 6372 6397 57_1624_1625|1,3311 57 1624 1625 57_176_185|0,1211 57 176 185 57_176_185|1,2111 57 176 185 1 5733_5644_8045|0,131322 5733 5644 8045 575_48_577|1,1332 575 48 577 5757_3476_6725|0,132213 5757 3476 6725 5763_5084_7685|0,123212 5763 5084 7685 5781_6460_8669|0,123232 5781 6460 8669 5785_1848_6073|0,122233 5785 1848 6073 583_1344_1465|1,2223 583 1344 1465 585_2072_2153|1,32211 585 2072 2153 585_928_1097|0,111331 585 928 1097 589_300_661|0,13323 589 300 661 59_1740_1741|1,3313 59 1740 1741 5917_2844_6565|0,131223 5917 2844 6565 6027_9964_11645|0,122231 6027 9964 11645 609_200_641|0,13233 609 200 641 61_1860_1861|1,3331 61 1860 1861 611_1020_1189|0,13231 611 1020 1189 611_1020_1189|1,31213 611 1020 1189 1 615_728_953|0,12332 615 728 953 615_728_953|1,3122 615 728 953 1 615_7552_7577|1,22333 615 7552 7577 621_100_629|1,13321 621 100 629 623_3936_3985|1,12233 623 3936 3985 627_364_725|0,11313 627 364 725 627_364_725|1,21212 627 364 725 1 629_540_829|0,13112 629 540 829 629_540_829|1,22121 629 540 829 1 63_16_65|0,1333 63 16 65 63_16_65|1,32 63 16 65 1 63_1984_1985|1,3333 63 1984 1985 6321_7120_9521|0,132232 6321 7120 9521 637_1116_1285|0,12131 637 1116 1285 6375_6512_9113|0,132122 6375 6512 9113 639_2480_2561|1,11233 639 2480 2561 6405_3652_7373|0,122313 6405 3652 7373 649_1680_1801|0,123311 649 1680 1801 65_2112_2113|1,11111 65 2112 2113 65_72_97|0,132 65 72 97 65_72_97|1,1211 65 72 97 1 651_4300_4349|1,32313 651 4300 4349 663_1216_1385|1,2323 663 1216 1385 663_616_905|0,13312 663 616 905 663_616_905|1,21122 663 616 905 1 665_432_793|0,12113 665 432 793 667_156_685|0,112333 667 156 685 667_156_685|1,2312 667 156 685 1 6695_3192_7417|0,112223 6695 3192 7417 67_2244_2245|1,11113 67 2244 2245 671_1800_1921|0,112311 671 1800 1921 671_1800_1921|1,32123 671 1800 1921 1 675_52_677|1,3112 675 52 677 6765_6052_9077|0,121212 6765 6052 9077 69_2380_2381|1,11131 69 2380 2381 69_260_269|0,13111 69 260 269 69_260_269|1,231 69 260 269 1 693_1924_2045|0,131311 693 1924 2045 693_1924_2045|1,13231 693 1924 2045 1 697_696_985|0,1222 697 696 985 7_24_25|0,111 7 24 25 7_24_25|1,3 7 24 25 1 703_504_865|1,12122 703 504 865 71_2520_2521|1,11133 71 2520 2521 713_216_745|0,111233 713 216 745 715_1428_1597|0,12121 715 1428 1597 7205_7068_10093|0,132322 7205 7068 10093 7239_6440_9689|0,132212 7239 6440 9689 725_108_733|1,31121 725 108 733 73_2664_2665|1,11311 73 2664 2665 731_780_1069|0,111132 731 780 1069 731_780_1069|1,31212 731 780 1069 1 7315_7332_10357|0,113222 7315 7332 10357 735_1088_1313|0,123331 735 1088 1313 735_1088_1313|1,3323 735 1088 1313 1 7383_3344_8105|0,122123 7383 3344 8105 741_1540_1709|0,13221 741 1540 1709 741_1540_1709|1,13221 741 1540 1709 1 741_580_941|1,12321 741 580 941 7421_15540_17221|0,122221 7421 15540 17221 747_3404_3485|1,32213 747 3404 3485 749_5700_5749|1,32331 749 5700 5749 75_2812_2813|1,11313 75 2812 2813 75_308_317|0,12111 75 308 317 75_308_317|1,2113 75 308 317 1 7521_3560_8321|0,123223 7521 3560 8321 759_2320_2441|0,131211 759 2320 2441 759_2320_2441|1,11223 759 2320 2441 1 759_280_809|0,12133 759 280 809 759_280_809|1,12132 759 280 809 1 765_868_1157|0,11232 765 868 1157 765_868_1157|1,12221 765 868 1157 1 767_1656_1825|0,111321 767 1656 1825 77_2964_2965|1,11331 77 2964 2965 77_36_85|0,123 77 36 85 77_36_85|1,321 77 36 85 1 775_168_793|1,21132 775 168 793 7755_8428_11453|0,122132 7755 8428 11453 777_464_905|0,11213 777 464 905 779_660_1021|0,12112 779 660 1021 781_2460_2581|0,112211 781 2460 2581 783_56_785|1,3132 783 56 785 79_3120_3121|1,11333 79 3120 3121 7923_8036_11285|0,123122 7923 8036 11285 793_1776_1945|0,113321 793 1776 1945 795_1292_1517|0,111231 795 1292 1517 795_1292_1517|1,33213 795 1292 1517 1 799_960_1249|0,113332 799 960 1249 799_960_1249|1,3322 799 960 1249 1 8023_3864_8905|0,121223 8023 3864 8905 803_2604_2725|0,123211 803 2604 2725 803_2604_2725|1,22213 803 2604 2725 1 805_348_877|1,23121 805 348 877 81_3280_3281|1,13111 81 3280 3281 8165_4092_9133|0,122323 8165 4092 9133 817_744_1105|0,11312 817 744 1105 819_1900_2069|1,23213 819 1900 2069 83_3444_3445|1,13113 83 3444 3445 8319_8200_11681|0,121322 8319 8200 11681 837_116_845|1,31321 837 116 845 847_7296_7345|1,32333 847 7296 7345 8479_7800_11521|0,122312 8479 7800 11521 85_132_157|0,1331 85 132 157 85_132_157|1,221 85 132 157 1 85_3612_3613|1,13131 85 3612 3613 851_420_949|0,11323 851 420 949 855_832_1193|0,13322 855 832 1193 855_832_1193|1,2322 855 832 1193 1 87_3784_3785|1,13133 87 3784 3785 87_416_425|0,131111 87 416 425 87_416_425|1,233 87 416 425 1 871_2160_2329|1,21223 871 2160 2329 89_3960_3961|1,13311 89 3960 3961 8925_4268_9893|0,132223 8925 4268 9893 893_924_1285|0,111122 893 924 1285 8967_8944_12665|0,131222 8967 8944 12665 897_496_1025|0,133313 897 496 1025 899_60_901|1,3312 899 60 901 9_40_41|0,1111 9 40 41 9_40_41|1,11 9 40 41 1 903_704_1145|1,2222 903 704 1145 909_5060_5141|1,32231 909 5060 5141 91_4140_4141|1,13313 91 4140 4141 91_60_109|0,1113 91 60 109 91_60_109|1,212 91 60 109 1 93_4324_4325|1,13331 93 4324 4325 93_476_485|0,121111 93 476 485 93_476_485|1,2131 93 476 485 1 931_1020_1381|0,13132 931 1020 1381 931_1020_1381|1,33212 931 1020 1381 1 935_1368_1657|1,11123 935 1368 1657 935_3552_3673|1,13233 935 3552 3673 943_576_1105|0,13213 943 576 1105 943_576_1105|1,3222 943 576 1105 1 945_248_977|0,131333 945 248 977 949_2580_2749|0,132311 949 2580 2749 949_2580_2749|1,31231 949 2580 2749 1 95_168_193|0,1131 95 168 193 95_168_193|1,123 95 168 193 1 95_4512_4513|1,13333 95 4512 4513 957_124_965|1,33121 957 124 965 969_1120_1481|0,111332 969 1120 1481 969_1480_1769|0,112331 969 1480 1769 97_4704_4705|1,31111 97 4704 4705 975_2728_2897|0,121311 975 2728 2897 975_448_1073|0,13123 975 448 1073 975_448_1073|1,3232 975 448 1073 1 987_884_1325|0,11212 987 884 1325 989_660_1189|0,131113 989 660 1189 99_20_101|0,13333 99 20 101 99_20_101|1,112 99 20 101 1 99_4900_4901|1,31113 99 4900 4901 9975_6032_11657|0,122213 9975 6032 11657 999_320_1049|0,12233 999 320 1049 999_320_1049|1,2232 999 320 1049 1

added triplets contained in both trees; regards Gangleri

Price's tree

Price's tree

all generations (0 to 6)
0 1 0 1 1 0 #Plato(0) #Pell(1,0) n/a 2 0	1 3 4 5 2 1 #Plato(1) #Pythagoras(1) #Pell(2,1) 3 1 4 4 12 2	1,1 5 12 13 3 2 #Plato(2) 5 1 12 9 30 4	1,11 9 40 41 5 4 #Plato(4) 9 1 40 25 90 8	1,111 17 144 145 9 8 #Plato(8) 17 1 144 81 306 16	1,1111 33 544 545 17 16 #Plato(16) 33 1 544 289 1122 32	1,11111 65 2112 2113 33 32 #Plato(32) 65 1 2112 1089 4290 64
						1,11112 1155 68 1157 34 1 #Pythagoras(17) 35 33 68 1156 2380 66
						1,11113 67 2244 2245 34 33 #Plato(33) 67 1 2244 1156 4556 66
					1,1112 323 36 325 18 1 #Pythagoras(9) 19 17 36 324 684 34	1,11121 357 76 365 19 2 21 17 76 361 798 68
						1,11122 1007 1224 1585 36 17 53 19 1224 1296 3816 646
						1,11123 935 1368 1657 36 19 55 17 1368 1296 3960 646 #p3b
					1,1113 35 612 613 18 17 #Plato(17) 35 1 612 324 1260 34	1,11131 69 2380 2381 35 34 #Plato(34 69 1 2380 1225 4830 68
						1,11132 1295 72 1297 36 1 #Pythagoras(18) 37 35 72 1296 2664 70
						1,11133 71 2520 2521 36 35 #Plato(35) 71 1 2520 1296 5112 70
				1,112 99 20 101 10 1 #Pythagoras(5) 11 9 20 100 220 18	1,1121 117 44 125 11 2 13 9 44 121 286 36	1,11211 153 104 185 13 4 17 9 104 169 442 72
						1,11212 403 396 565 22 9 31 13 396 484 1364 234
						1,11213 315 572 653 22 13 35 9 572 484 1540 234
					1,1122 319 360 481 20 9 29 11 360 400 1160 198	1,11221 517 1044 1165 29 18 47 11 1044 841 2726 396
						1,11222 1479 880 1721 40 11 51 29 880 1600 4080 638
						1,11223 759 2320 2441 40 29 69 11 2320 1600 5520 638
					1,1123 279 440 521 20 11 31 9 440 400 1240 198	1,11231 477 1364 1445 31 22 53 9 1364 961 3286 396
						1,11232 1519 720 1681 40 9 49 31 720 1600 3920 558
						1,11233 639 2480 2561 40 31 71 9 2480 1600 5680 558
				1,113 19 180 181 10 9 #Plato(9) 19 1 180 100 380 18	1,1131 37 684 685 19 18 #Plato(18) 37 1 684 361 1406 36	1,11311 73 2664 2665 #c3b1 37 36 #Plato(36) 73 1 2664 1369 5402 72
						1,11312 1443 76 1445 38 1 #Pythagoras(19) 39 37 76 1444 2964 74
						1,11313 75 2812 2813 38 37 #Plato(37) 75 1 2812 1444 5700 74 #p2b
					1,1132 399 40 401 20 1 #Pythagoras(10) 21 19 40 400 840 38	1,11321 437 84 445 21 2 23 19 84 441 966 76
						1,11322 1239 1520 1961 40 19 59 21 1520 1600 4720 798
						1,11323 1159 1680 2041 40 21 61 19 1680 1600 4880 798
					1,1133 39 760 761 20 19 #Plato(19) 39 1 760 400 1560 38	1,11331 77 2964 2965 39 38 #Plato(38) 77 1 2964 1521 6006 76
						1,11332 1599 80 1601 40 11 #Pythagoras(20) 41 39 80 1600 3280 78
						1,11333 79 3120 3121 40 39 #Plato(39) 79 1 3120 1600 6320 78
			1,12 35 12 37 6 1 #Pythagoras(3) 7 5 12 36 84 10	1,121 45 28 53 7 2 9 5 28 49 126 20	1,1211 65 72 97 9 4 13 5 72 81 234 40	1,12111 105 208 233 13 8 21 5 208 169 546 80
						1,12112 299 180 349 18 5 23 13 180 324 828 130
						1,12113 155 468 493 18 13 31 5 468 324 1116 130
					1,1212 171 140 221 14 5 19 9 140 196 532 90	1,12121 261 380 461 19 10 29 9 380 361 1102 180
						1,12122 703 504 865 28 9 37 19 504 784 2072 342
						1,12123 423 1064 1145 28 19 47 9 1064 784 2632 342
					1,1213 115 252 277 14 9 23 5 252 196 644 90	1,12131 205 828 853 23 18 41 5 828 529 1886 180
						1,12132 759 280 809 28 5 33 23 280 784 1848 230
						1,12133 255 1288 1313 28 23 51 5 1288 784 2856 230
				1,122 119 120 169 12 5 #Pell(4,3) 17 7 120 144 408 70	1,1221 189 340 389 17 10 27 7 340 289 918 140	1,12211 329 1080 1129 27 20 47 7 1080 729 2538 280
						1,12212 1107 476 1205 34 7 41 27 476 1156 2788 378
						1,12213 427 1836 1885 34 27 61 7 1836 1156 4148 378
					1,1222 527 336 625 24 7 31 17 336 576 1488 238	1,12221 765 868 1157 31 14 45 17 868 961 2790 476
						1,12222 2015 1632 2593 48 17 65 31 1632 2304 6240 1054
						1,12223 1343 2976 3265 48 31 79 17 2976 2304 7584 1054
					1,1223 287 816 865 24 17 41 7 816 576 1968 238	1,12231 525 2788 2837 41 34 75 7 2788 1681 6150 476
						1,12232 2255 672 2353 48 7 55 41 672 2304 5280 574
						1,12233 623 3936 3985 48 41 89 7 3936 2304 8544 574
				1,123 95 168 193 12 7 19 5 168 144 456 70	1,1231 165 532 557 19 14 33 5 532 361 1254 140	1,12311 305 1848 1873 33 28 61 5 1848 1089 4026 280
						1,12312 1419 380 1469 38 5 43 33 380 1444 3268 330
						1,12313 355 2508 2533 38 33 71 5 2508 1444 5396 330
					1,1232 551 240 601 24 5 29 19 240 576 1392 190	1,12321 741 580 941 29 10 39 19 580 841 2262 380
						1,12322 1943 1824 2665 #c3b1 48 19 69 29 1824 2304 6432 1102
						1,12323 1463 2784 3145 48 29 77 19 2784 2304 7392 1102
					1,1233 215 912 937 24 19 43 5 912 576 2064 190	1,12331 405 3268 3293 43 38 81 5 3268 1849 6966 380
						1,12332 2279 480 2329 48 5 53 43 480 2304 5088 430
						1,12333 455 4128 4153 48 43 91 5 4128 2304 8736 430
			1,13 11 60 61 6 5 #Plato(5) 11 1 60 36 132 10	1,131 21 220 221 11 10 #Plato(10) 21 1 220 121 462 20	1,1311 41 840 841 21 20 #Plato(20) 41 1 840 441 1722 40	1,13111 81 3280 3281 41 40 #Plato(40) 81 1 3280 1681 6642 80
						1,13112 1763 84 1765 42 1 #Pythagoras(21) 43 41 84 1764 3612 82
						1,13113 83 3444 3445 42 41 #Plato(41) 83 1 3444 1764 6972 82
					1,1312 483 44 485 22 1 #Pythagoras(11) 23 21 44 484 1012 42	1,13121 525 92 533 23 2 25 21 92 529 1150 84
						1,13122 1495 1848 2377 44 21 65 23 1848 1936 5720 966 #p5b
						1,13123 1407 2024 2465 44 23 67 21 2024 1936 5896 966
					1,1313 43 924 925 22 21 #Plato(21) 43 1 924 484 1892 42	1,13131 85 3612 3613 43 42 #Plato(42) 85 1 3612 1849 7310 84
						1,13132 1935 88 1937 44 1 #Pythagoras(22) 45 43 b n 3960 86 #p3b
						1,13133 87 3784 3785 44 43 #Plato(43) 87 1 88 1936 7656 86
				1,132 143 24 145 12 1 #Pythagoras(6) 13 11 24 144 312 22	1,1321 165 52 173 13 2 15 11 b n 390 44	1,13211 209 120 241 15 4 19 11 b n 570 88
1,13212 555 572 797 26 11 37 15 b n 1924 330
1,13213 451 780 901 26 15 41 11 b n 2132 330
1,1322 455 528 697 24 11 53 13 b n 1680 286	1,13221 741 1540 1709 35 22 57 13 b n 3990 572
	1,13222 2135 1248 2473 48 13 61 53 b n 5856 910
	1,13223 1079 3360 3529 48 35 83 13 b n 7968 910
1,1323 407 624 745 24 13 37 11 b n 1776 286	1,13231 693 1924 2045 37 26 63 11 b n 4662 572
	1,13232 2183 1056 2425 48 11 59 37 b n 5664 814
	1,13233 935 3552 3673 48 37 85 11 b n 8160 814
1,133 23 264 265 12 11 #Plato(11) 23 1 b n 552 22	1,1331 45 1012 1013 23 22 #Plato(22) 45 1 b n 2070 44	1,13311 89 3960 3961 45 44 #Plato(44) 89 1 b n 8010 88
		1,13312 2115 92 2117 46 1 #Pythagoras(23) 47 45 b n 4324 90
		1,13313 91 4140 4141 46 45 #Plato(45) 91 1 b n 8372 90
	1,1332 575 48 577 24 1 #Pythagoras(12) 25 23 b n 1200 46	1,13321 621 100 629 25 2 27 23 b n 1350 92
		1,13322 1775 2208 2833 48 23 71 25 b n 6816 1150
		1,13323 1679 2400 2929 48 25 73 23 b n 7008 1150
	1,1333 47 1104 1105 24 23 #Plato(23) 47 1 b n 2256 46	1,13331 93 4324 4325 47 46 #Plato(46) 93 1 b n 8742 92
		1,13332 2303 96 2305 48 1 #Pythagoras(24) 49 47 b n 4704 94
		1,13333 95 4512 4513 48 47 #Plato(47) 95 1 b n 9120 94
1,2 15 8 17 4 1 #Pythagoras(2) 5 3 b n 40 6	1,21 21 20 29 5 2 #Pell(3,2) 7 3 b n 70 12	1,211 33 56 65 7 4 11 3 b n 154 24	1,2111 57 176 185 11 8 19 3 b n 418 48	1,21111 105 608 617 19 16 35 3 b n 1330 96
				1,21112 475 132 493 22 3 25 19 b n 1100 114
				1,21113 123 836 845 22 19 41 3 b n 1804 114
			1,2112 187 84 205 14 3 17 11 b n 476 66	1,21121 253 204 325 17 6 23 11 b n 782 132
				1,21122 663 616 905 28 11 39 17 b n 2184 374
				1,21123 495 952 1073 28 17 45 11 b n 2520 374
			1,2113 75 308 317 14 11 25 3 b n 700 66	1,21131 141 1100 1109 25 22 47 3 b n 2350 132
				1,21132 775 168 793 28 3 31 25 b n 1736 150
				1,21133 159 1400 1409 28 25 53 3 b n 2968 150
		1,212 91 60 109 10 3 13 7 b n 260 42	1,2121 133 156 205 13 6 19 7 b n 494 84	1,21211 217 456 505 19 12 31 7 b n 1178 168
				1,21212 627 364 725 26 7 33 19 b n 1716 266 #p1b
				1,21213 315 988 1037 26 19 45 7 b n 2340 266
			1,2122 351 280 449 20 7 27 13 b n 1080 182	1,21221 533 756 925 27 14 41 13 b n 2214 364
				1,21222 1431 1040 1769 40 13 53 27 b n 4240 702
				1,21223 871 2160 2329 40 27 67 13 b n 5360 702
			1,2123 231 520 569 20 13 33 7 b n 1320 182	1,21231 413 1716 1765 33 26 59 7 b n 3894 364
				1,21232 1551 560 1649 40 7 47 33 b n 3760 462
				1,21233 511 2640 2689 40 33 73 7 b n 5840 462
		1,213 51 140 149 10 7 17 3 b n 340 42	1,2131 93 476 485 17 14 31 3 b n 1054 84	1,21311 177 1736 1745 31 28 59 3 b n 3658 168
				1,21312 1147 204 1165 34 3 37 31 b n 2516 186
				1,21313 195 2108 2117 34 31 65 3 b n 4420 186
			1,2132 391 120 409 20 3 23 17 b n 920 102	1,21321 493 276 565 23 6 29 17 b n 1334 204
				1,21322 1311 1360 1889 40 17 57 23 b n 4560 782
				1,21323 1071 1840 2129 40 23 63 17 b n 5040 782
			1,2133 111 680 689 20 17 37 3 b n 1480 102	1,21331 213 2516 2525 37 34 71 3 b n 5254 204
				1,21332 1591 240 1609 40 3 43 37 b n 3440 222
				1,21333 231 2960 2969 40 37 77 3 b n 6160 222
	1,22 55 48 73 8 3 11 5 b n 176 30	1,221 85 132 157 11 6 17 5 b n 374 60	1,2211 145 408 433 17 12 29 5 b n 986 120	1,22111 265 1392 1417 29 24 53 5 b n 3074 240
				1,22112 1131 340 1181 34 5 39 29 b n 2652 290 #p2b
				1,22113 315 1972 1997 34 29 63 5 b n 4284 290
			1,2212 459 220 509 22 5 27 17 b n 1188 170	1,22121 629 540 829 27 10 37 17 b n 1998 340
				1,22122 1647 1496 2225 44 17 61 27 b n 5368 918
				1,22123 1207 2376 2665 #c3b1 44 27 71 17 b n 6248 918
			1,2213 195 748 773 22 17 39 5 b n 1716 170 #p1b	1,22131 365 2652 2677 39 34 73 5 b n 5694 340
				1,22132 1911 440 1961 44 5 49 39 b n 4312 390
				1,22133 415 3432 3457 44 39 83 5 b n 7304 390
		1,222 231 160 281 16 5 21 11 b n 672 110	1,2221 341 420 541 21 10 31 11 b n 1302 220	1,22211 561 1240 1361 31 20 51 11 b n 3162 440
				1,22212 1643 924 1885 42 11 53 31 b n 4452 682
				1,22213 803 2604 2725 42 31 73 11 b n 6132 682
			1,2222 903 704 1145 32 11 43 21 b n 2752 462	1,22221 1365 1892 2333 43 22 65 21 b n 5590 924
				1,22222 3655 2688 4537 64 21 85 43 b n 10880 1806
				1,22223 2247 5504 5945 64 43 107 21 b n 13696 1806
			1,2223 583 1344 1465 32 21 53 11 b n 3392 462	1,22231 1045 4452 4573 53 42 95 11 b n 10070 924
				1,22232 3975 1408 4217 64 11 75 53 b n 9600 1166
				1,22233 1287 6784 6905 64 53 117 11 b n 14976 1166
		1,223 135 352 377 16 11 27 5 b n 864 110	1,2231 245 1188 1213 27 22 49 5 b n 2646 220	1,22311 465 4312 4337 49 44 93 5 b n 9114 440
				1,22312 2891 540 2941 54 5 59 49 b n 6372 490
				1,22313 515 5292 5317 54 49 103 5 b n 11124 490
			1,2232 999 320 1049 32 5 37 27 b n 2368 270	1,22321 1269 740 1469 37 10 47 27 b n 3478 540
				1,22322 3367 3456 4825 64 27 91 37 b n 11648 1998
				1,22323 2727 4736 5465 64 37 101 27 b n 12928 1998
			1,2233 295 1728 1753 32 27 59 5 b n 3776 270	1,22331 565 6372 6397 59 54 113 5 b n 13334 540
				1,22332 4071 640 4121 64 5 69 59 b n 8832 590
				1,22333 615 7552 7577 64 59 123 5 b n 15744 590
	1,23 39 80 89 8 5 13 3 b n 208 30	1,231 69 260 269 13 10 23 3 b n 598 60	1,2311 129 920 929 23 20 43 3 b n 1978 120	1,23111 249 3440 3449 43 40 83 3 b n 7138 240
				1,23112 2107 276 2125 46 3 49 43 b n 4508 258
				1,23113 267 3956 3965 46 43 89 3 b n 8188 258
			1,2312 667 156 685 26 3 29 23 b n 1508 138	1,23121 805 348 877 29 6 35 23 b n 2030 276
				1,23122 2175 2392 3233 52 23 75 29 b n 7800 1334
				1,23123 1863 3016 3545 52 29 81 23 b n 8424 1334
			1,2313 147 1196 1205 26 23 49 3 b n 2548 138	1,23131 285 4508 4517 49 46 95 3 b n 9310 276
				1,23132 2695 312 2713 52 3 55 49 b n 5720 294 #p5b
				1,23133 303 5096 5105 52 49 101 3 b n 10504 294
		1,232 247 96 265 16 3 19 13 b n 608 78	1,2321 325 228 397 19 6 25 13 b n 950 156	1,23211 481 600 769 25 12 37 13 b n 1850 312
1,23212 1275 988 1613 38 13 51 v b n 3876 650
1,23213 819 1900 2069 38 25 63 13 b n 4788 650
1,2322 855 832 1193 32 13 45 19 b n 2880 494			1,23221 1349 2340 2701 45 26 71 19 b n 6390 988
			1,23222 3735 2432 4457 64 19 83 45 b n 10624 1710
			1,23223 2071 5760 6121 64 45 109 19 b n 13952 1710
1,2323 663 1216 1385 32 19 51 13 b n 3264 494			1,23231 1157 3876 4045 51 38 89 13 b n 9078 988
			1,23232 3927 1664 4265 64 13 77 51 b n 9856 1326
			1,23233 1495 6528 6697 64 51 115 13 b n 14720 1326
1,233 87 416 425 16 13 29 3 b n 928 78		1,2331 165 1508 1517 29 26 55 3 b n 3190 156	1,23311 321 5720 5729 55 52 107 3 b n 11770 312
			1,23312 3355 348 3373 58 3 61 55 b n 7076 330
			1,23313 339 6380 6389 58 55 113 3 b n 13108 330
		1,2332 1015 192 1033 32 3 35 29 b n 2240 174	1,23321 1189 420 1261 35 6 41 29 b n 2870 348
			1,23322 3255 3712 4937 64 29 93 35 b n 11904 2030
			1,23323 2871 4480 5321 64 35 99 29 b n 12672 2030
		1,2333 183 1856 1865 32 29 61 3 b n 3904 174	1,23331 357 7076 7085 61 58 119 3 b n 14518 348
			1,23332 4087 384 4105 64 3 67 61 b n 8576 366
			1,23333 375 7808 7817 64 61 125 3 b n 16000 366
1,3 7 24 25 4 3 #Plato(3) 7 1 b n 56 6	1,31 13 84 85 7 6 #Plato(6) 13 1 b n 182 12	1,311 25 312 313 13 12 #Plato(12) 25 1 b n 650 24	1,3111 49 1200 1201 25 24 #Plato(24) 49 1 b n 2450 48	1,31111 97 4704 4705 49 48 #Plato(48) 97 1 b n 9506 96
				1,31112 2499 100 2501 50 1 #Pythagoras(25) 51 49 b n 5100 98
				1,31113 99 4900 4901 50 49;nbsp;#Plato(49) 99 1 b n 9900 98
			1,3112 675 52 677 26 1 #Pythagoras(13) 27 25 b n 1404 50	1,31121 725 108 733 27 2 29 25 b n 1566 100
				1,31122 2079 2600 3329 52 25 77 27 b n 8008 1350
				1,31123 1975 2808 3433 52 27 79 25 b n 8216 1350
			1,3113 51 1300 1301 26 25 #Plato(25) 51 1 b n 2652 50 #p2b	1,31131 101 5100 5101 51 50 #Plato(50) 101 1 b n 10302 100
				1,31132 2703 104 2705 52 1 #Pythagoras(26) 53 51 b n 5512 102
				1,31133 103 5304 5305 52 51 #Plato(51) 103 1 b n 10712 102
		1,312 195 28 197 14 1 #Pythagoras(7) 15 13 b n 420 26	1,3121 221 60 229 15 2 17 13 b n 510 52	1,31211 273 136 305 17 4 21 13 b n 714 104
				1,31212 731 780 1069 30 13 43 17 b n 2580 442
				1,31213 611 1020 1189 30 17 47 13 b n 2820 442
			1,3122 615 728 953 28 13 41 15 b n 2296 390	1,31221 1005 2132 2357 41 26 67 15 b n 5494 780
				1,31222 2911 1680 3361 56 15 71 41 b n 7952 1230
				1,31223 1455 4592 4817 56 41 97 15 b n 10864 1230
			1,3123 559 840 1009 28 15 43 13 b n 2408 390	1,31231 949 2580 2749 43 30 73 13 b n 6278 780
				1,31232 2967 1456 3305 56 13 69 43 b n 7728 1118
				1,31233 1287 4816 4985 56 43 99 13 b n 11088 1118
		1,313 27 364 365 14 13 #Plato(13) 27 1 b n 756 26	1,3131 53 1404 1405 27 26 #Plato(26) 53 1 b n 2862 52	1,31311 105 5512 5513 53 52 #Plato(52) 105 1 b n 11130 104
				1,31312 2915 108 2917 54 1 #Pythagoras(27) 55 53 b n 5940 106
				1,31313 107 5724 5725 54 53 #Plato(53) 107 1 b n 11556 106
			1,3132 783 56 785 28 1 #Pythagoras(14) 29 27 b n 1624 54	1,31321 837 116 845 29 2 31 29 b n 1798 108
				1,31322 2407 3024 3865 56 27 83 27 b n 9296 1566
				1,31323 2295 3248 3977 56 29 85 29 b n 9520 1566
			1,3133 55 1512 1513 28 27 #Plato(27) 55 1 b n 3080 54	1,31331 109 5940 5941 55 54 #Plato(54) 109 1 b n 11990 108
				1,31332 3135 112 3137 56 1 #Pythagoras(28) 57 55 b n 6384 110
				1,31333 111 6160 6161 56 55 #Plato(55) 111 1 b n 12432 110
	1,32 63 16 65 8 1 #Pythagoras(4) 9 7 b n 144 14	1,321 77 36 85 9 2 11 7 b n 198 28	1,3211 105 88 137 11 4 15 7 b n 330 56	1,32111 161 240 289 15 8 23 7 b n 690 112
				1,32112 435 308 533 22 7 29 15 b n 1276 210
				1,32113 259 660 709 22 15 37 7 b n 1628 210
			1,3212 275 252 373 18 7 25 11 b n 900 154	1,32121 429 700 821 25 14 39 11 b n 1950 308
				1,32122 1175 792 1417 36 11 47 25 b n 3384 550
				1,32123 671 1800 1921 36 25 61 11 b n 4392 550
			1,3213 203 396 445 18 11 29 7 b n 1044 154	1,32131 357 1276 1325 29 22 51 7 b n 2958 308
				1,32132 1247 504 1345 36 7 43 29 b n 3096 406
				1,32133 455 2088 2137 36 29 65 7 b n 4680 406
		1,322 207 224 305 16 7 23 9 b n 736 126	1,3221 333 644 725 23 14 37 9 b n 1702 252	1,32211 585 2072 2153 37 28 65 9 b n 4810 504
				1,32212 2035 828 2197 46 9 55 37 b n 5060 666
				1,32213 747 3404 3485 46 37 83 9 b n 7636 666
			1,3222 943 576 1105 32 9 41 23 b n 2624 414	1,32221 1357 1476 2005 41 18 59 23 b n 4838 828
				1,32222 3567 2944 4625 64 23 97 41 b n 11136 1886
				1,32223 2415 5248 5777 64 41 105 23 b n 13440 1886
			1,3223 495 1472 1553 32 23 55 9 b n 3520 414	1,32231 909 5060 5141 55 46 101 9 b n 11110 828
				1,32232 4015 1152 4177 64 9 73 55 b n 9344 990
				1,32233 1071 7040 7121 64 55 119 9 b n 15232 990
		1,323 175 288 337 16 9 25 7 b n 800 126	1,3231 301 900 949 25 18 43 7 b n 2150 252	1,32311 553 3096 3145 43 36 79 7 b n 6794 504
				1,32312 2451 700 2549 50 7 57 43 b n 5700 602 #p4b
				1,32313 651 4300 4349 50 43 93 7 b n 9300 602
			1,3232 975 448 1073 32 7 39 25 b n 2496 350	1,32321 1325 1092 1717 39 14 53 25 b n 4134 700
				1,32322 3471 3200 4721 64 25 89 39 b n 11392 1950
				1,32323 2575 4992 5617 64 39 103 25 b n 13184 1950
			1,3233 399 1600 1649 32 25 57 7 b n 3648 350	1,32331 749 5700 5749 57 50 107 7 b n 12198 700
				1,32332 4047 896 4145 64 7 71 57 b n 9088 798
				1,32333 847 7296 7345 64 57 121 7 b n 15488 798
	1,33 15 112 113 8 7 #Plato(7) 15 1 b n 240 14	1,331 29 420 421 15 14 #Plato(14) 29 1 b n 870 28	1,3311 57 1624 1625 29 28 #Plato(28) 57 1 b n 3306 56	1,33111 113 6384 6385 57 56 #Plato(56) 113 1 b n 12882 112
				1,33112 3363 116 3365 58 1 #Pythagoras(29) 59 57 b n 6844 114
				1,33113 115 6612 6613 58 57 #Plato(57) 115 1 b n 13340 114
			1,3312 899 60 901 30 1 #Pythagoras(15) 31 29 b n 1860 58	1,33121 957 124 965 31 2 33 29 b n 2046 116
				1,33122 2759 3480 4441 60 29 89 31 b n 10680 1798
				1,33123 2639 3720 4561 60 31 91 29 b n 10920 1798
			1,3313 59 1740 1741 30 29 #Plato(29) 59 1 b n 3540 58	1,33131 117 6844 6845 59 58 #Plato(58) 117 1 b n 13806 116
				1,33132 3599 120 3601 60 1 #Pythagoras(30) 61 59 b n 7320 118
				1,33133 119 7080 7081 60 59 #Plato(59) 119 1 b n 14280 118
		1,332 255 32 257 16 1 #Pythagoras(8) 17 15 b n 544 30	1,3321 285 68 293 17 2 19 15 b n 646 60	1,33211 345 152 377 19 4 23 15 b n 874 120
1,33212 931 1020 1381 34 15 49 19 b n 3332 570
1,33213 795 1292 1517 34 19 53 15 b n 3604 570
1,3322 799 960 1249 32 15 47 17 b n 3008 510			1,33221 1309 2820 3109 47 30 77 17 b n 7238 1020
			1,33222 3807 2176 4385 64 17 81 47 b n 10368 1598
			1,33223 1887 6016 6305 64 47 b n 111 17 14208 1598
1,3323 735 1088 1313 32 17 49 15 b n 3136 510			1,33231 1245 3332 3557 49 34 83 15 b n 8134 1020
			1,33232 3871 1920 4321 64 15 79 49 b n 10112 1470
			1,33233 1695 6272 6497 64 49 113 15 b n 14464 1470
1,333 31 480 481 16 15 #Plato(17) 31 1 b n 992 30		1,3331 61 1860 1861 31 30 #Plato(30) 61 1 b n 3782 60	1,33311 121 7320 7321 61 60 #Plato(60) 121 1 b n 14762 120
			1,33312 3843 124 3845 62 1 #Pythagoras(31) 63 61 b n 7812 122
			1,33313 123 7564 7565 62 61 #Plato(61) 123 1 b n 15252 122
		1,3332 1023 64 1025 32 1 #Pythagoras(16) 33 31 b n 2112 62	1,33321 1085 132 1093 33 2 35 31 b n 2310 124
			1,33322 3135 3968 5057 64 31 95 33 b n 12160 2046
			1,33323 3007 4224 5185 64 33 97 31 b n 12416 2046
		1,3333 63 1984 1985 32 31 #Plato(31) 63 1 b n 4032 62	1,33331 125 7812 7813 63 62 #Plato(62) 125 1 b n 15750 124
			1,33332 4095 128 4097 64 1 #Pythagoras(32) 65 63 b n 8320 126
			1,33333 127 8064 8065 64 63 #Plato(63) 127 1 b n 16256 126
top of table

details to Price's tree

to be continued 2A02:810D:41C0:134:6C5D:2ACF:DA6:D533 (talk) 18:07, 12 July 2019 (UTC)

---

sorted (b, n) pairs for the Price's tree

0 1 4 4 12 9 40 25 144 81 544 289 2112 1089 68 1156 2244 1156 36 324 76 361 1224 1296 1368 1296 612 324 2380 1225 72 1296 2520 1296 20 100 44 121 104 169 396 484 572 484 360 400 1044 841 880 1600 2320 1600 440 400 1364 961 720 1600 2480 1600 180 100 684 361 2664 1369 76 1444 2812 1444 40 400 84 441 1520 1600 1680 1600 760 400 2964 1521 80 1600 3120 1600 12 36 28 49 72 81 208 169 180 324 468 324 140 196 380 361 504 784 1064 784 252 196 828 529 280 784 1288 784 120 144 340 289 1080 729 476 1156 1836 1156 336 576 868 961 1632 2304 2976 2304 816 576 2788 1681 672 2304 3936 2304 168 144 532 361 1848 1089 380 1444 2508 1444 240 576 580 841 1824 2304 2784 2304 912 576 3268 1849 480 2304 4128 2304 60 36 220 121 840 441 3280 1681 84 1764 3444 1764 44 484 92 529 1848 1936 2024 1936 924 484 3612 1849 88 1936 3784 1936 24 144 52 169 120 225 572 676 780 676 528 576 1540 1225 1248 2304 3360 2304 624 576 1924 1369 1056 2304 3552 2304 264 144 1012 529 3960 2025 92 2116 4140 2116 48 576 100 625 2208 2304 2400 2304 1104 576 4324 2209 96 2304 4512 2304 8 16 20 25 56 49 176 121 608 361 132 484 836 484 84 196 204 289 616 784 952 784 308 196 1100 625 168 784 1400 784 60 100 156 169 456 361 364 676 988 676 280 400 756 729 1040 1600 2160 1600 520 400 1716 1089 560 1600 2640 1600 140 100 476 289 1736 961 204 1156 2108 1156 120 400 276 529 1360 1600 1840 1600 680 400 2516 1369 240 1600 2960 1600 48 64 132 121 408 289 1392 841 340 1156 1972 1156 220 484 540 729 1496 1936 2376 1936 748 484 2652 1521 440 1936 3432 1936 160 256 420 441 1240 961 924 1764 2604 1764 704 1024 1892 1849 2688 4096 5504 4096 1344 1024 4452 2809 1408 4096 6784 4096 352 256 1188 729 4312 2401 540 2916 5292 2916 320 1024 740 1369 3456 4096 4736 4096 1728 1024 6372 3481 640 4096 7552 4096 80 64 260 169 920 529 3440 1849 276 2116 3956 2116 156 676 348 841 2392 2704 3016 2704 1196 676 4508 2401 312 2704 5096 2704 96 256 228 361 600 625 988 1444 1900 1444 832 1024 2340 2025 2432 4096 5760 4096 1216 1024 3876 2601 1664 4096 6528 4096 416 256 1508 841 5720 3025 348 3364 6380 3364 192 1024 420 1225 3712 4096 4480 4096 1856 1024 7076 3721 384 4096 7808 4096 24 16 84 49 312 169 1200 625 4704 2401 100 2500 4900 2500 52 676 108 729 2600 2704 2808 2704 1300 676 5100 2601 104 2704 5304 2704 28 196 60 225 136 289 780 900 1020 900 728 784 2132 1681 1680 3136 4592 3136 840 784 2580 1849 1456 3136 4816 3136 364 196 1404 729 5512 2809 108 2916 5724 2916 56 784 116 841 3024 3136 3248 3136 1512 784 5940 3025 112 3136 6160 3136 16 64 36 81 88 121 240 225 308 484 660 484 252 324 700 625 792 1296 1800 1296 396 324 1276 841 504 1296 2088 1296 224 256 644 529 2072 1369 828 2116 3404 2116 576 1024 1476 1681 2944 4096 5248 4096 1472 1024 5060 3025 1152 4096 7040 4096 288 256 900 625 3096 1849 700 2500 4300 2500 448 1024 1092 1521 3200 4096 4992 4096 1600 1024 5700 3249 896 4096 7296 4096 112 64 420 225 1624 841 6384 3249 116 3364 6612 3364 60 900 124 961 3480 3600 3720 3600 1740 900 6844 3481 120 3600 7080 3600 32 256 68 289 152 361 1020 1156 1292 1156 960 1024 2820 2209 2176 4096 6016 4096 1088 1024 3332 2401 1920 4096 6272 4096 480 256 1860 961 7320 3721 124 3844 7564 3844 64 1024 132 1089 3968 4096 4224 4096 1984 1024 7812 3969 128 4096 8064 4096

added sorted (b, n) pairs for the Price's tree; regards Gangleri 217.86.249.144 (talk) 14:34, 16 July 2019 (UTC)

updated sorted properly by path no bias — קיין אומוויסנדיק פּרעפֿערענצן — keyn umvisndik preferentsn ^{talk contribs} 12:27, 19 July 2019 (UTC)

getting harassed by a nasty excell sort bug no bias — קיין אומוויסנדיק פּרעפֿערענצן — keyn umvisndik preferentsn ^{talk contribs} 13:16, 19 July 2019 (UTC)

now replaced with values for the Price tree no bias — קיין אומוויסנדיק פּרעפֿערענצן — keyn umvisndik preferentsn ^{talk contribs} 13:28, 19 July 2019 (UTC)

getting harassed by a nasty excell sort bug; using fake number workaround no bias — קיין אומוויסנדיק פּרעפֿערענצן — keyn umvisndik preferentsn ^{talk contribs} 13:50, 19 July 2019 (UTC)

comments

from user:לערי ריינהארט/sandbox; regards Gangleri 2A02:810D:41C0:134:6C5D:2ACF:DA6:D533 (talk) 18:07, 12 July 2019 (UTC)

like Cronus, Wikipedia devours its children

regards Gangleri 217.86.249.144 (talk) 15:09, 16 July 2019 (UTC)

to do

consider:

rational triangles a redirect to integer triangles;

rational trigonometry not considered here further

triangles where all trigonometric values of the three angles ^{see also trigonometric functions: sine, cosine, tangent, and their reciprocals cosecant, secant and cotangent} are rational numbers; these are Pythagorean triangles ^{redirecting to Pythagorean triple}.

the six values for the trigonometric functions: sine, cosine, tangent, and their reciprocals cosecant, secant and cotangent are keys ^{(cryptography)} each enabeling to identify a unique primitive Pythagorean triple ^{today a redirect to Pythagorean triple; a better redirect could be tree of primitive Pythagorean triples; the later should be moved to trees of primitive Pythagorean triples}; the representation of the rational number values associated with each trigonometric function would be the pair of two integer numbers used to codify the rational number as a fraction
So far 13 keys for each primitive Pythagorean triple are identified. It is a bias issue of each contributor how many and which to be used.
regards Gangleri 95.91.248.133 (talk) 10:29, 17 July 2019 (UTC)

Pythagorean numbers a redirect to Pythagorean prime

Pythagorean pair / Pythagorean pairs referred in file:Pythagorean pairs.svg

regards no bias — קיין ומוויסנדיק פּרעפֿערענצן — keyn umvisndik preferentsn ^{talk contributions} 20:47, 17 July 2019 (UTC)