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A005850 Primes p such that the NSW number A002315((p-1)/2) is prime.
(Formerly M2426)
2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

REFERENCES

P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 290.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=1..25.

M. Newman, D. Shanks, 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

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 *)

PROG

(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

CROSSREFS

Cf. A002315.

A099088 is a closely related sequence.

Sequence in context: A079131 A179687 A106919 * A052334 A154526 A126144

Adjacent sequences:  A005847 A005848 A005849 * A005851 A005852 A005853

KEYWORD

nonn,nice,hard

AUTHOR

N. J. A. Sloane.

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

STATUS

approved

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Last modified July 25 23:14 EDT 2014. Contains 244919 sequences.