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%I #21 Jan 27 2023 15:26:59
%S 3,19,31,691,907,2887,15943,69283,216127,1108831,8344423,10976347,
%T 166965391,385465771,26580643
%N Smallest k such that 2^(3*2^n) + k is a safe prime.
%C a(n) == 3 (mod 4). - _Chai Wah Wu_, Jan 27 2023
%F a(n) = A350696(3*2^n).
%e a(1) = 19 because 2^(3*2^1)+19 = 2^6+19 = 83 is the smallest safe prime greater than 64.
%o (PARI) a(n) = {my(k=1); pow2 = 2^(3*2^n); while (!(isprime(pow2 + k) && isprime((pow2 + k - 1)/2)), k+=2); k;} \\
%o (Python)
%o from sympy import isprime, nextprime
%o def A360081(n):
%o m = 1<<3*(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. A360080, A335313, A350696, A005385, A013597, A013603, A181356, A057821.
%K nonn,more,hard
%O 0,1
%A _Mark Andreas_, Jan 25 2023
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