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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. 6

%I

%S 1,2,5,9,14,29,30,35,39,50,65,69,90,99,135,174,189,204,224,230,260,

%T 284,285,315,320,330,369,375,410,440,464,495,515,519,525,534,545,564,

%U 575,585,590,680,719,729,744,749,765,854,870,905,915,950,974,1080,1119

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

%C 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 Zak Seidov, <a href="/A068501/b068501.txt">Table of n, a(n) for n = 1..10000</a>

%H Robert Simms, <a href="http://www.math.clemson.edu/~rsimms/neat/math/pyth">Pythagorean Triples Generator</a>

%t lst={};Do[If[PrimeQ[(n+1)^2-n^2]&&PrimeQ[(n+1)^2+n^2],AppendTo[lst,n]],{n,7!}];lst [From _Vladimir Joseph Stephan Orlovsky_, Jun 01 2010]

%t 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 Cf. A051892.

%K nonn

%O 1,2

%A _Lekraj Beedassy_, Mar 25 2002

%E More terms from Larry Reeves (larryr(AT)acm.org), Jun 19 2002

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Last modified October 25 15:08 EDT 2014. Contains 248556 sequences.