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A165158
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Hypotenuses of primitive Pythagorean triangles such that all 3 sides are composite.
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3
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65, 85, 125, 145, 169, 185, 205, 221, 265, 289, 305, 325, 365, 377, 425, 445, 481, 485, 493, 505, 533, 545, 565, 625, 629, 685, 689, 697, 725, 745, 785, 793, 845, 865, 901, 905, 925, 949, 965, 985, 1025, 1037, 1073, 1105, 1145, 1157, 1165, 1189, 1205, 1241
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OFFSET
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1,1
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COMMENTS
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Numbers C in triples of the form A^2+B^2=C^2, gcd(A,B,C)=1 and all of A, B and C in A002808.
If multiple solutions exist for the same C, as for example (A,B,C) = (16,63,65) and (33,56,65),
only one instance of C is added to the sequence.
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LINKS
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EXAMPLE
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(A,B,C) = (16,63,65), (36,77,85), (44,117,125) etc
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MATHEMATICA
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lst={}; Do[Do[If[IntegerQ[a=Sqrt[c^2-b^2]]&&GCD[a, b, c]==1, If[a>=b, Break[]]; If[ !PrimeQ[a]&&!PrimeQ[b]&&!PrimeQ[c], AppendTo[lst, c]]], {b, c-1, 4, -1}], {c, 5, 2000, 1}]; Union@lst
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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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Typo in description corrected by Alan Frank, Oct 09 2009
Definition clarified, comment moved to the examples and new comment added - R. J. Mathar, Oct 21 2009
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STATUS
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approved
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