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A074236
Numbers that are the long leg of some integer right triangle and the hypotenuse of some other integer right triangle.
0
15, 20, 30, 35, 40, 45, 52, 55, 60, 68, 70, 75, 80, 90, 91, 100, 104, 105, 110, 116, 117, 120, 135, 136, 140, 143, 148, 150, 153, 156, 160, 164, 165, 175, 180, 182, 187, 195, 200, 204, 208, 210, 212, 220, 221, 225, 232, 234, 240, 244, 245, 247, 255, 260, 270
OFFSET
1,1
COMMENTS
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.
Note that all terms are composite.
FORMULA
Intersection of A009012 and A009003.
EXAMPLE
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.
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A066860 A120159 A163602 * A086770 A111200 A088494
KEYWORD
nonn
AUTHOR
Zak Seidov, Sep 18 2002
EXTENSIONS
Corrected by Harvey P. Dale, Apr 26 2012
STATUS
approved