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%I #19 Jan 29 2024 19:12:33
%S 15,20,30,35,40,45,52,55,60,68,70,75,80,90,91,100,104,105,110,116,117,
%T 120,135,136,140,143,148,150,153,156,160,164,165,175,180,182,187,195,
%U 200,204,208,210,212,220,221,225,232,234,240,244,245,247,255,260,270
%N Numbers that are the long leg of some integer right triangle and the hypotenuse of some other integer right triangle.
%C A009003 gives ordered values of hypotenuses of integer right triangles; A009012 gives ordered values of long legs of integer right triangles. Their intersection is this sequence.
%C Note that all terms are composite.
%F Intersection of A009012 and A009003.
%e 15 is a term because it is the long leg of the integer right triangle with sides 8, 15, 17 and the hypotenuse of the integer right triangle with sides 9, 12, 15.
%t prims=With[{cps=Select[Subsets[Range[1,221,2],{2}],CoprimeQ@@#&]}, ptrip[ {a_,b_}]:={a*b,(b^2-a^2)/2,(b^2+a^2)/2};Sort[Sort/@(ptrip/@cps)]]; pyths= Sort[Flatten[Table[n #&/@prims,{n,200}],1]]; Take[Intersection[ Transpose[ pyths][[2]],Transpose[pyths][[3]]],80] (* _Harvey P. Dale_, Apr 26 2012 *)
%Y Cf. A009003, A009012.
%K nonn
%O 1,1
%A _Zak Seidov_, Sep 18 2002
%E Corrected by _Harvey P. Dale_, Apr 26 2012
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