A005850 Primes p such that the NSW number A002315((p-1)/2) is prime.

3, 5, 7, 19, 29, 47, 59, 163, 257, 421, 937, 947, 1493, 1901, 6689, 8087, 9679, 28753, 79043, 129127, 145969, 165799, 168677, 170413, 172243

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• hard
• more

Comments

Some of the larger entries may only correspond to probable primes.

References

• Paulo Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 290.
• Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 248.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• M. Newman, D. Shanks, and H. Williams, Simple groups of square order and interesting sequence of primes, Acta Arithmetica (1980), Volume: 38, Issue: 2, page 129-140
• Eric Weisstein's World of Mathematics, Pell Number
• Eric Weisstein's World of Mathematics, Pythagoras's Constant

Crossrefs

Cf. A002315, A088165.

A099088 is a closely related sequence.

Programs

Mathematica

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 *)

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

Formula

A088165(n) mod a(n) = 1. - Altug Alkan, Mar 17 2016

Extensions

6689, 8087, 9679 reported by Warut Roonguthai on the PrimeForm mailing list.

28753 found by Andrew Walker (ajw01(AT)uow.edu.au), Jul 12 2001.

129127, 145969, 165799, 168677, 170413, 172243 found by Eric W. Weisstein, May 22 2006 - Jan 25 2007 [from Mike Oakes, Mar 29 2009]

Name corrected by David Applegate, Jean-François Alcover and Charles R Greathouse IV, Oct 19 2012