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A360080
Smallest k such that 2^(2^n) + k is a safe prime.
2
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
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
KEYWORD
nonn,more,hard
AUTHOR
Mark Andreas, Jan 25 2023
STATUS
approved