login
A165159
Long legs in primitive Pythagorean triangles with three side lengths of composite integers.
3
56, 63, 77, 117, 120, 143, 153, 156, 171, 176, 187, 220, 224, 240, 247, 253, 273, 304, 323, 345, 352, 357, 360, 364, 377, 396, 403, 416, 435, 437, 456, 460, 468, 475, 476, 483, 493, 513, 525, 527, 528, 544, 561, 621, 624, 627, 644, 663, 665, 667, 672, 680
OFFSET
1,1
COMMENTS
The sequence collects the numbers B such that A^2+B^2=C^2, A<B<C, gcd(A,B,C)=1 and such that all
three of A, B and C are in A002808. If there are two or more triangles of this kind with the same B,
like (A,B,C) = (1003,1596,1885) and (A,B,C) = (1403,1596,2125), only one instance
of B is added to the sequence.
EXAMPLE
(A,B,C)=(33,56,65) contributes B=56 to the sequence. (A,B,C)=(16,63,65) contributes B=63 to the sequence.
MATHEMATICA
lst={}; Do[Do[If[IntegerQ[c=Sqrt[a^2+b^2]] && GCD[a, b, c]==1, If[ !PrimeQ[a]&&!PrimeQ[b] && !PrimeQ[c], AppendTo[lst, b]]], {a, b-1, 3, -1}], {b, 4, 2000, 1}]; Union@lst
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited by R. J. Mathar, Oct 02 2009
STATUS
approved