%I #22 Jan 29 2023 17:52:24
%S 1,7,7,7,91,3103,12451,230191,286867,1657867,10029811,29761351,
%T 22410151,98402791,167137543
%N Smallest k such that 2^(2^n) + k is a safe prime.
%C a(n) == 3 (mod 4) for n > 1. - _Chai Wah Wu_, Jan 27 2023
%F a(n) = A350696(2^n).
%e a(3) = 7 because 2^(2^3) + 7 = 263 is the smallest safe prime greater than 256.
%o (PARI) a(n) = {my(k=1); pow2 = 2^(2^n); while (!(isprime(pow2 + k) && isprime((pow2 + k - 1)/2)), k+=2); k;} \\
%o (Python)
%o from sympy import isprime, nextprime
%o def A360080(n):
%o if n <= 1: return 1
%o m = 1<<(1<<n)-1
%o i = m
%o while i:=nextprime(i):
%o if isprime(k:=(i<<1)+1):
%o return k-(m<<1) # _Chai Wah Wu_, Jan 27 2023
%Y Cf. A360081, A181356, A005385, A058220, A013597, A013603, A335313, A350696.
%K nonn,more,hard
%O 1,2
%A _Mark Andreas_, Jan 25 2023