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%I #15 Apr 05 2020 21:10:22
%S 15,35,39,45,51,65,69,85,95,105,141,145,159,165,175,195,205,209,221,
%T 231,245,255,261,275,279,285,299,309,315,325,329,345,371,375,391,399,
%U 415,425,435,455,459,465,471,519,535,545,555,559,561,575,581,585,595
%N Odd numbers that are the right-angle adjacent side in more than one primitive Pythagorean triple with prime hypotenuse
%H Robert Israel, <a href="/A154988/b154988.txt">Table of n, a(n) for n = 1..6000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Pythagorean_triple"> Pythagorean triple</a>
%H Eric Rowland, <a href="https://ericrowland.github.io/investigations/tripleslist-long.html">Primitive Integral Solutions to x^2 + y^2 = z^2</a>
%e 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.
%p 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:
%p select(filter, [seq(i,i=1..1000, 2)]); # _Robert Israel_, Aug 30 2016
%K nonn
%O 1,1
%A Avik Roy (avik_3.1416(AT)yahoo.co.in), Jan 18 2009
%E Data corrected by _Robert Israel_, Aug 30 2016
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