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A154988
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Odd numbers that are the right-angle adjacent side in more than one primitive Pythagorean triple with prime hypotenuse
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1
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15, 35, 39, 45, 51, 65, 69, 85, 95, 105, 141, 145, 159, 165, 175, 195, 205, 209, 221, 231, 245, 255, 261, 275, 279, 285, 299, 309, 315, 325, 329, 345, 371, 375, 391, 399, 415, 425, 435, 455, 459, 465, 471, 519, 535, 545, 555, 559, 561, 575, 581, 585, 595
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OFFSET
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1,1
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LINKS
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EXAMPLE
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165 exists in 3 Pythagorean triples as right-angle adjacent side, (165, 52, 173), (165, 532, 557), (165, 1508, 1517); among these the first two have prime hypotenuse.
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MAPLE
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filter:= x -> nops(select(t -> subs(t, y)>0 and subs(t, z) > 0 and isprime(subs(t, z)), [isolve(x^2=z^2-y^2)]))>1:
select(filter, [seq(i, i=1..1000, 2)]); # Robert Israel, Aug 30 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Avik Roy (avik_3.1416(AT)yahoo.co.in), Jan 18 2009
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EXTENSIONS
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STATUS
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approved
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