A066179 Primes p such that (p-1)/2 and (p-3)/4 are also prime.

11, 23, 47, 167, 359, 719, 1439, 2039, 2879, 4079, 4127, 4919, 5639, 5807, 5927, 6047, 7247, 7559, 7607, 7727, 9839, 10799, 11279, 13799, 13967, 14159, 15287, 15647, 20327, 21599, 21767, 23399, 24407, 24527, 25799, 28319, 28607, 29399

Offset

1,1

Comments

Call p "m-prime" iff (p-(2^i-1))/2^i is prime for i=0..m; sequence gives 2-primes. 0-primes are primes (A000040) and 1-primes are safe primes (A005385). a(n)-1 and a(n) are consecutive terms of the sequence A065966. It is not known if there are infinitely many m-primes for m > 0.

Links

Harry J. Smith, Table of n, a(n) for n=1,...,1000

Mathematica

lst={}; Do[p=Prime[n]; If[PrimeQ[a=(p-1)/2]&&PrimeQ[(a-1)/2], AppendTo[lst, p]], {n, 8!}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 27 2009 *)

Prog

(PARI) { n=0; default(primelimit, 4294965247); for (m=1, 10^9, p=prime(m); if (frac((p-3)/4), next); if (isprime((p-3)/4) && isprime((p-1)/2), write("b066179.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Feb 05 2010

Crossrefs

Cf. A000040, A005385, A065966.

Sequence in context: A100558 A126199 A096342 * A217566 A347141 A278869

Adjacent sequences: A066176 A066177 A066178 * A066180 A066181 A066182

Keyword

nonn

Author

Vladeta Jovovic, Dec 14 2001

Extensions

Offset changed from 0 to 1 by Harry J. Smith, Feb 05 2010

Status

approved