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%I M2426 #30 Mar 17 2016 10:43:54
%S 3,5,7,19,29,47,59,163,257,421,937,947,1493,1901,6689,8087,9679,28753,
%T 79043,129127,145969,165799,168677,170413,172243
%N Primes p such that the NSW number A002315((p-1)/2) is prime.
%C Some of the larger entries may only correspond to probable primes.
%D P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 290.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H M. Newman, D. Shanks, H. Williams, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa38/aa3826.pdf">Simple groups of square order and interesting sequence of primes</a>, Acta Arithmetica (1980), Volume: 38, Issue: 2, page 129-140
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PellNumber.html">Pell Number</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PythagorassConstant.html">Pythagoras's Constant</a>
%F A088165(n) mod a(n) = 1. - _Altug Alkan_, Mar 17 2016
%t max = 10000 (* computation is very slow beyond this limit *); nc = Numerator[Convergents[Sqrt[2], max]]; Reap[Do[If[PrimeQ[n], If[PrimeQ[nc[[n]]], Print[n]; Sow[n]]] , {n, 3, max}]][[2, 1]] (* _Jean-François Alcover_, Oct 22 2012, after _David Applegate_ *)
%o (PARI) is(n)=my(w=3+quadgen(32)); isprime(n) && n>2 && ispseudoprime(imag((1+w)*w^(n\2))) \\ _Charles R Greathouse IV_, Oct 19 2012
%Y Cf. A002315, A088165.
%Y A099088 is a closely related sequence.
%K nonn,nice,hard
%O 1,1
%A _N. J. A. Sloane_
%E 6689, 8087, 9679 reported by Warut Roonguthai on the PrimeForm mailing list.
%E 28753 found by Andrew Walker (ajw01(AT)uow.edu.au), Jul 12 2001.
%E 129127, 145969, 165799, 168677, 170413, 172243 found by _Eric W. Weisstein_, May 22 2006 - Jan 25 2007 [from _Mike Oakes_, Mar 29 2009]
%E Name corrected by _David Applegate_, _Jean-François Alcover_ and _Charles R Greathouse IV_, Oct 19 2012
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