A360080 Smallest k such that 2^(2^n) + k is a safe prime.

1, 7, 7, 7, 91, 3103, 12451, 230191, 286867, 1657867, 10029811, 29761351, 22410151, 98402791, 167137543

Offset

1,2

Comments

a(n) == 3 (mod 4) for n > 1. - Chai Wah Wu, Jan 27 2023

Links

Table of n, a(n) for n=1..15.

Formula

a(n) = A350696(2^n).

Example

a(3) = 7 because 2^(2^3) + 7 = 263 is the smallest safe prime greater than 256.

Prog

(PARI) a(n) = {my(k=1); pow2 = 2^(2^n);   while (!(isprime(pow2 + k) && isprime((pow2 + k - 1)/2)), k+=2); k; } \\
(Python)
from sympy import isprime, nextprime
def A360080(n):
    if n <= 1: return 1
    m = 1<<(1<<n)-1
    i = m
    while i:=nextprime(i):
        if isprime(k:=(i<<1)+1):
            return k-(m<<1) # Chai Wah Wu, Jan 27 2023

Crossrefs

Cf. A360081, A181356, A005385, A058220, A013597, A013603, A335313, A350696.

Sequence in context: A117981 A024955 A328824 * A352712 A088467 A153496

Adjacent sequences: A360077 A360078 A360079 * A360081 A360082 A360083

Keyword

nonn,more,hard

Author

Mark Andreas, Jan 25 2023

Status

approved