A165159 Long legs in primitive Pythagorean triangles with three side lengths of composite integers.

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.

Links

Table of n, a(n) for n=1..52.

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

Cf. A020882, A020883, A165158, A165160.

Sequence in context: A069810 A292896 A154768 * A336265 A039428 A043251

Adjacent sequences: A165156 A165157 A165158 * A165160 A165161 A165162

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Sep 06 2009

Extensions

Edited by R. J. Mathar, Oct 02 2009

Status

approved