A345014 a(n) is the least nonnegative integer k such that 2^n - k is a Sophie Germain prime.

0, 1, 3, 5, 3, 11, 15, 5, 3, 5, 9, 23, 81, 83, 135, 143, 9, 23, 117, 5, 9, 161, 159, 317, 339, 203, 219, 95, 693, 35, 105, 5, 321, 425, 69, 23, 201, 191, 219, 983, 1101, 371, 747, 287, 429, 743, 2649, 1355, 81, 233, 237, 635, 2403, 395, 1125, 1997, 69, 9005

Offset: 1

Author

Artsiom Palkounikau, Sep 15 2021

Keywords

• nonn

Links

• Artsiom Palkounikau, Table of n, a(n) for n = 1..3072

Crossrefs

Cf. A005384, A057821, A013603, A243916.

Programs

Mathematica

Table[k=0;While[!(PrimeQ[p=2^n-k]&&PrimeQ[2p+1]),k++];k,{n,58}] (* Giorgos Kalogeropoulos, Sep 15 2021 *)

PARI

a(n) = my(k=0,p); while (!(isprime(p=2^n-k) && isprime(2*p+1)), k++); k; \\ Michel Marcus, Sep 15 2021

Python

from sympy import isprime
def a(n):
    k = 0
    while True:
        if isprime(2 ** n - k) and isprime(2 * (2 ** n - k) + 1):
            return k
        k += 1
print([a(i) for i in range(1, 21)])

Formula

a(n) = (A057821(n+1) + 1)/2.