A332940 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.

29, 11, 47, 59, 83, 317, 227, 251, 311, 503, 263, 587, 383, 503, 419, 503, 1997, 647, 599, 911, 863, 983, 1187, 1031, 1019, 1163, 1223, 1319, 1451, 3083, 1511, 1583, 1523, 1559, 3923, 2399, 3203, 2063, 2939, 2099, 2243, 2243, 2591, 3359, 2903, 2963, 3023, 2939, 2999

Offset

1,1

Links

Table of n, a(n) for n=1..49.

WonTae Hwang and Kyunghwan Song, Absolutely simple polarized abelian varieties of odd Sophie Germain prime dimension over finite fields with maximal automorphism groups, arXiv:2002.12353 [math.NT], 2020. See Lemma 3.1.

Example

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

Prog

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

Crossrefs

Cf. A005384 (Sophie Germain primes).

Sequence in context: A040816 A336061 A160494 * A165769 A040815 A033349

Adjacent sequences: A332937 A332938 A332939 * A332941 A332942 A332943

Keyword

nonn

Author

Michel Marcus, Mar 03 2020

Status

approved