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

Author

Vladimir Joseph Stephan Orlovsky, Sep 06 2009

Keywords

• nonn

Comments

The sequence collects the numbers B such that A^2+B^2=C^2, A

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.

Examples

			(A,B,C)=(33,56,65) contributes B=56 to the sequence. (A,B,C)=(16,63,65) contributes B=63 to the sequence.
		

Crossrefs

Cf. A020882, A020883, A165158, A165160.

Programs

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

Extensions

Edited by R. J. Mathar, Oct 02 2009

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