

A005850


Primes p such that the NSW number A002315((p1)/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
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OFFSET

1,1


COMMENTS

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


REFERENCES

P. Ribenboim, The Book of Prime Number Records. SpringerVerlag, 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 129140
Eric Weisstein's World of Mathematics, Pell Number
Eric Weisstein's World of Mathematics, Pythagoras's Constant


FORMULA

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


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]] (* JeanFrançois 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, A088165.
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, JeanFrançois Alcover and Charles R Greathouse IV, Oct 19 2012


STATUS

approved



