A157358 Triple-safe primes p: p, (p-1)/2, (p-3)/4, and (p-7)/8 are all prime.

23, 47, 719, 1439, 2879, 4079, 9839, 11279, 21599, 28319, 51599, 84719, 92399, 95279, 96959, 137279, 157679, 159119, 178799, 209519, 219839, 243119, 349199, 429119, 430799, 441839, 462719, 481199, 491279, 507359, 533999, 571199, 597599

Offset

1,1

Comments

These occur in a proof of nonexistence of a certain type of permutation group for p (Theorem 8 by Ito). - R. J. Mathar, May 29 2011

Links

Table of n, a(n) for n=1..33.

Noboru Ito, Transitive permutation groups of degree p=2q+1, p and q being prime numbers, Bull. AMS 69 (2) (1963), 165-192.

Formula

a(n) >> n log^(4) n. - Charles R Greathouse IV, Oct 14 2021

Example

(23-1)/2=11, (11-1)/2=5, (5-1)/2=2(prime), ...

Mathematica

lst={}; Do[p=Prime[n]; If[PrimeQ[a=(p-1)/2]&&PrimeQ[b=(a-1)/2]&&PrimeQ[(b-1)/2], AppendTo[lst, p]], {n, 9!}]; lst

Prog

(PARI) is(n)=n%8==7 && isprime(n) && isprime(n\2) && isprime(n\4) && isprime(n\8) \\ Charles R Greathouse IV, Oct 14 2021
(PARI) list(lim)=my(v=List()); forprimestep(p=23, lim\1, 8, if(isprime(p\8) && isprime(p\4) && isprime(p\2), listput(v, p))); Vec(v); \\ Charles R Greathouse IV, Oct 14 2021

Crossrefs

Cf. A005385, A066179, A157357.

Sequence in context: A042054 A084667 A255596 * A158238 A328799 A333115

Adjacent sequences: A157355 A157356 A157357 * A157359 A157360 A157361

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Feb 27 2009

Status

approved