A367966 - OEIS

%I #33 Jan 14 2024 12:39:49

%S 2,2,5,11,23,41,83,131,281,593,1031,2063,4211,8243,16421,32771,65633,

%T 131321,262193,524351,1048889,2097629,4194581,8388953,16777259,

%U 33554771,67108913,134218433,268435631,536871311,1073741891,2147483693,4294967681,8589934631,17179869659

%N Smallest Sophie Germain prime >= 2^n.

%H Robert Israel, <a href="/A367966/b367966.txt">Table of n, a(n) for n = 0..1000</a>

%F Apparently a(n) = (A111671(n) - 1)/2 for n>=2. - _Hugo Pfoertner_, Dec 13 2023

%e 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 For n = 1, a(1) = 2 because 2 is prime, 2*(2) + 1 = 5 is prime, 2 >= 2^1 where 2^1 = 2.

%e 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 a:= proc(n) option remember; local p; for p from 2^n

%p       while not andmap(isprime, [p, 2*p+1]) do od; p

%p     end:

%p seq(a(n), n=0..44);  # _Alois P. Heinz_, Dec 13 2023

%t 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 (PARI) a(n) = forprime(p=2^n, , if (isprime(2*p+1), return(p))); \\ _Michel Marcus_, Dec 12 2023

%Y Cf. A104080, A005384.

%K nonn

%O 0,1

%A _Andrei Lapets_, Dec 06 2023