A023330 Primes that remain prime through 5 iterations of function f(x) = 2x + 1.

89, 63419, 127139, 405269, 810809, 1069199, 1122659, 1178609, 1333889, 1598699, 1806089, 1958249, 2164229, 2245319, 2329469, 2606069, 2848949, 3241289, 3339989, 3784199, 3962039, 4088879, 4328459, 4444829, 4658939, 4664249, 4894889, 4897709, 5132999

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Primes p such that 2*p+1, 4*p+3, 8*p+7, 16*p+15 and 32*p+31 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A005384, A005385, A007700, A023272, A023302, A057331, A005602.

Programs

Magma

[n: n in [1..5000000] | forall{2^i*n+2^i-1: i in [0..5] | IsPrime(2^i*n+2^i-1)}]; // Vincenzo Librandi, Aug 04 2010

Mathematica

Select[Prime[Range[10^5]], PrimeQ[a1=2*#+1] && PrimeQ[a2=2*a1+1] && PrimeQ[a3=2*a2+1] && PrimeQ[a4=2*a3+1] && PrimeQ[a5=2*a4+1] &] (* Vladimir Joseph Stephan Orlovsky, May 01 2008 *)

PARI

is(n)=isprime(n) && isprime(2*n+1) && isprime(4*n+3) && isprime(8*n+7) && isprime(16*n+15) && isprime(32*n+31) \\ Charles R Greathouse IV, Jul 01 2013

Python

from sympy import prime, isprime
A023330_list = [p for p in (prime(n) for n in range(1,10**5)) if all([isprime(2**m*(p+1)-1) for m in range(1,6)])] # Chai Wah Wu, Sep 09 2014

Formula

a(n) == 29 (mod 30). - Zak Seidov, Jan 31 2013