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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. 8
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 24 06:17 EDT 2021. Contains 345416 sequences. (Running on oeis4.)