A360081 Smallest k such that 2^(3*2^n) + k is a safe prime.

3, 19, 31, 691, 907, 2887, 15943, 69283, 216127, 1108831, 8344423, 10976347, 166965391, 385465771, 26580643

Offset

0,1

Comments

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

Links

Table of n, a(n) for n=0..14.

Formula

a(n) = A350696(3*2^n).

Example

a(1) = 19 because 2^(3*2^1)+19 = 2^6+19 = 83 is the smallest safe prime greater than 64.

Prog

(PARI) a(n) = {my(k=1); pow2 = 2^(3*2^n); while (!(isprime(pow2 + k) && isprime((pow2 + k - 1)/2)), k+=2); k; } \\
(Python)
from sympy import isprime, nextprime
def A360081(n):
    m = 1<<3*(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. A360080, A335313, A350696, A005385, A013597, A013603, A181356, A057821.

Sequence in context: A162307 A128069 A056246 * A061427 A069516 A098856

Adjacent sequences: A360078 A360079 A360080 * A360082 A360083 A360084

Keyword

nonn,more,hard

Author

Mark Andreas, Jan 25 2023

Status

approved