A376946 - OEIS

%I #17 Nov 09 2024 11:54:53

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

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

%C a(7) > 46472.

%C a(7) > 2*10^7. - _Michael S. Branicky_, Nov 09 2024

%t Table[m = 3;

%t  k = 0; Monitor[

%t   Parallelize[

%t    While[True,

%t     If[And[PrimeQ[m^((m + 1)*m^n) - k],

%t       PrimeQ[((m^((m + 1)*m^n) - k) - 1)/2]], Break[]]; k++]; k],

%t   k], {n, 0, 5}]

%o (PARI) a(n) = {my(k=0); while (!(isprime(p=3^(4*3^n) - k) && isprime((p-1)/2)), k++); k;}

%o (Python)

%o from sympy import isprime, prevprime

%o def A(n):

%o     m = 3**(4*3**n)

%o     p = prevprime(m)

%o     while not isprime((p-1)//2):

%o         p = prevprime(p)

%o     return m-p #

%Y Cf. A005385, A057821, A181356, A335313.

%K nonn,more

%O 0,1

%A _J.W.L. (Jan) Eerland_, Oct 10 2024