A376946 Smallest k such that 3^(4*3^n) - k is a safe prime.

22, 202, 6934, 634, 109678, 445294, 2323138

Offset: 0

Author

J.W.L. (Jan) Eerland, Oct 10 2024

Keywords

• nonn
• more

Comments

a(7) > 46472.

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

Crossrefs

Cf. A005385, A057821, A181356, A335313.

Programs

Mathematica

Table[m = 3;
 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=3^(4*3^n) - k) && isprime((p-1)/2)), k++); k;}

Python

from sympy import isprime, prevprime
def A(n):
    m = 3**(4*3**n)
    p = prevprime(m)
    while not isprime((p-1)//2):
        p = prevprime(p)
    return m-p #