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

1, 2, 5, 9, 14, 29, 30, 35, 39, 50, 65, 69, 90, 99, 135, 174, 189, 204, 224, 230, 260, 284, 285, 315, 320, 330, 369, 375, 410, 440, 464, 495, 515, 519, 525, 534, 545, 564, 575, 585, 590, 680, 719, 729, 744, 749, 765, 854, 870, 905, 915, 950, 974, 1080, 1119

Offset

1,2

Comments

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.

Links

Zak Seidov, Table of n, a(n) for n = 1..10000

Robert Simms, Deriving Pythagorean Triples (web archive)

Mathematica

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 *)
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 *)

Crossrefs

Cf. A051892.

Sequence in context: A325717 A291942 A071609 * A048071 A320996 A051892

Adjacent sequences: A068498 A068499 A068500 * A068502 A068503 A068504

Keyword

nonn

Author

Lekraj Beedassy, Mar 25 2002

Extensions

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

Status

approved