A377724 Smallest k such that 4^(5*4^n) - k is a safe prime.

5, 437, 13709, 40169, 574133

Offset: 0

Author

J.W.L. (Jan) Eerland, Nov 05 2024

Keywords

• nonn
• more

Comments

a(5) > 2*10^7. - Michael S. Branicky, Nov 09 2024

Crossrefs

Cf. A005385, A057821, A181356, A335313, A376946.

Programs

Mathematica

Table[m = 4;
 k = 0; Monitor[
  Parallelize[
   While[True,
    If[And[PrimeQ[m^((m + 1)*m^n) - k],
      PrimeQ[((m^((m + 1)*m^n) - k) - 1)/2]], Break[]]; k++]; k],k], {n, 0, 5}]

PARI

a(n) = {my(k=0); while (!(isprime(p=4^(5*4^n) - k) && isprime((p-1)/2)), k++); k;}

Python

from sympy import isprime, prevprime
def A(n):
    m = 4**(5*4**n)
    p = prevprime(m)
    while not isprime((p-1)//2):
        p = prevprime(p)
    return m-p #