A117673 - OEIS

%I #29 Dec 01 2023 17:33:39

%S 1,1,1,2,1,2,3,5,1,1,5,2,1,2,3,1,6,3,2,4,2,2,1,1,2,3,3,3,5,1,2,1,3,2,

%T 4,3,5,2,7,1,1,3,1,2,9,2,5,6,12,6,1,1,3,1,3,3,4,3,2,1,3,1,2,3,3,13,3,

%U 5,3,5,7,1,3,2,6,6,12,3,4,2,1,5,1,2,5,1,4,15,3,6,3,4,2,1,2,3,1,16,5,9

%N a(n) is the least k such that k*2*prime(n) + 1 is prime.

%C Iff a(n) = 1, prime(n) is a Sophie Germain prime, i.e., in A005384. - _A.H.M. Smeets_, Feb 01 2018

%H Zak Seidov, <a href="/A117673/b117673.txt">Table of n, a(n) for n = 1..10000</a>

%e a(8)=5 because 2*prime(8)=38 and 5*38 + 1 is prime.

%t Table[k := 1; While[ ! PrimeQ[2*k*Prime[n] + 1], k++ ]; k, {n, 1, 120}] (* _Stefan Steinerberger_, May 01 2006 *)

%o (PARI) a(n) = {my(p=prime(n), k=1); while (!isprime(2*k*p+1), k++); k;} \\ _Michel Marcus_, Feb 12 2018

%Y Cf. A016014, A035096, A074884.

%K nonn

%O 1,4

%A _Don Reble_, Apr 25 2006