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A068501 Values m such that the consecutive pair parameters(m,m+1) generate Pythagorean triples whose odd terms are both prime.

%I A068501 #15 Jan 27 2020 17:36:58
%S A068501 1,2,5,9,14,29,30,35,39,50,65,69,90,99,135,174,189,204,224,230,260,
%T A068501 284,285,315,320,330,369,375,410,440,464,495,515,519,525,534,545,564,
%U A068501 575,585,590,680,719,729,744,749,765,854,870,905,915,950,974,1080,1119
%N A068501 Values m such that the consecutive pair parameters(m,m+1) generate Pythagorean triples whose odd terms are both prime.
%C A068501 Setting u=m; v=m+1, triples (a,b,c) with a=u+v, b=2*u*v, c = u^2+v^2 = (a^2+1)/2 correspond to (A048161, A067755, A067756), a and c being both prime.
%H A068501 Zak Seidov, <a href="/A068501/b068501.txt">Table of n, a(n) for n = 1..10000</a>
%H A068501 Robert Simms, <a href="https://web.archive.org/web/20080622012348/http://www.math.clemson.edu/~simms/neat/math/pyth/">Deriving Pythagorean Triples</a> (web archive)
%t A068501 lst={};Do[If[PrimeQ[(n+1)^2-n^2]&&PrimeQ[(n+1)^2+n^2],AppendTo[lst,n]],{n,7!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jun 01 2010 *)
%t A068501 Reap[Do[a=Prime[k];If[PrimeQ[(a^2+1)/2],Sow[(a-1)/2]],{k,2,10^5}]][[2,1]](* _Zak Seidov_, Apr 16 2011 *)
%Y A068501 Cf. A051892.
%K A068501 nonn
%O A068501 1,2
%A A068501 _Lekraj Beedassy_, Mar 25 2002
%E A068501 More terms from Larry Reeves (larryr(AT)acm.org), Jun 19 2002