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A074236
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Numbers that are the long leg of some integer right triangle and the hypotenuse of some other integer right triangle.
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0
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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FORMULA
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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