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A367966 Smallest Sophie Germain prime >= 2^n.

%I A367966 #33 Jan 14 2024 12:39:49
%S A367966 2,2,5,11,23,41,83,131,281,593,1031,2063,4211,8243,16421,32771,65633,
%T A367966 131321,262193,524351,1048889,2097629,4194581,8388953,16777259,
%U A367966 33554771,67108913,134218433,268435631,536871311,1073741891,2147483693,4294967681,8589934631,17179869659
%N A367966 Smallest Sophie Germain prime >= 2^n.
%H A367966 Robert Israel, <a href="/A367966/b367966.txt">Table of n, a(n) for n = 0..1000</a>
%F A367966 Apparently a(n) = (A111671(n) - 1)/2 for n>=2. - _Hugo Pfoertner_, Dec 13 2023
%e A367966 For n = 0, a(0) = 2 because 2 is prime, 2*(2) + 1 = 5 is prime, 2 >= 2^0 where 2^0 = 1, and 1 is not prime.
%e A367966 For n = 1, a(1) = 2 because 2 is prime, 2*(2) + 1 = 5 is prime, 2 >= 2^1 where 2^1 = 2.
%e A367966 For n = 2, a(2) = 5 because 5 is prime, 2*(5) + 1 = 11 is prime, 5 >= 2^2 where 2^2 = 4, and 4 is not prime.
%p A367966 a:= proc(n) option remember; local p; for p from 2^n
%p A367966       while not andmap(isprime, [p, 2*p+1]) do od; p
%p A367966     end:
%p A367966 seq(a(n), n=0..44);  # _Alois P. Heinz_, Dec 13 2023
%t A367966 a={}; nmax=35; For[n=0, n<=nmax, n++, k=2^n; While[!PrimeQ[k] || !PrimeQ[2k+1], k++]; AppendTo[a,k]]; a (* _Stefano Spezia_, Dec 10 2023 *)
%o A367966 (PARI) a(n) = forprime(p=2^n, , if (isprime(2*p+1), return(p))); \\ _Michel Marcus_, Dec 12 2023
%Y A367966 Cf. A104080, A005384.
%K A367966 nonn
%O A367966 0,1
%A A367966 _Andrei Lapets_, Dec 06 2023