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

1,3

Links

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A005384, A057821, A013603, A243916.

Sequence in context: A089730 A351368 A105445 * A328878 A178095 A177904

Adjacent sequences: A345011 A345012 A345013 * A345015 A345016 A345017

Keyword

nonn

Author

Artsiom Palkounikau, Sep 15 2021

Status

approved