%I #6 Mar 03 2020 06:56:38

%S 29,11,47,59,83,317,227,251,311,503,263,587,383,503,419,503,1997,647,

%T 599,911,863,983,1187,1031,1019,1163,1223,1319,1451,3083,1511,1583,

%U 1523,1559,3923,2399,3203,2063,2939,2099,2243,2243,2591,3359,2903,2963,3023,2939,2999

%N a(n) is the least prime p such that p = x^2 + (2g+1)*y^2 and p != 2*g+1 and p mod (2g+1) != 1 where g is the n-th Sophie Germain prime.

%H WonTae Hwang and Kyunghwan Song, <a href="https://arxiv.org/abs/2002.12353">Absolutely simple polarized abelian varieties of odd Sophie Germain prime dimension over finite fields with maximal automorphism groups</a>, arXiv:2002.12353 [math.NT], 2020. See Lemma 3.1.

%e For g=A005384(1)=2, 2g+1 is 5, we have 29 = 9 + 5*4 and 29 != 5, and 29 mod 5 != 1.

%o (PARI) f(g) = {my(p = 2); while (1, my(s = 1); while(s^2 < p/(2*g+1), if (issquare(p - (2*g+1)*s^2), if ((p != 2*g+1) && (Mod(p, 2*g+1) != 1), return(p););); s++;); p = nextprime(p+1););}

%o lista(nn) = {forprime(g=2, nn, if (isprime(2*g+1), print1(f(g), ", ")););}

%Y Cf. A005384 (Sophie Germain primes).

%K nonn

%O 1,1

%A _Michel Marcus_, Mar 03 2020