A257362 Odd primes modulo which -163 is a square.

41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 163, 167, 173, 179, 197, 199, 223, 227, 251, 263, 281, 307, 313, 347, 359, 367, 373, 379, 383, 397, 409, 419, 421, 439, 457, 461, 487, 499, 503, 523, 547, 563, 577, 593, 607, 641, 647, 653, 661, 673, 677, 691

Offset: 1

Author

Robert Israel, Apr 20 2015

Keywords

• nonn
• easy

Comments

Contains A005846. The first members that are not in A005846 are 163 and 167.

Primes that divide some member of A202018.

Primes congruent to x^2 mod 163 for some x, 0 <= x <= 162.

Primes of the form x^2 + xy + 41y^2. Also, primes of the form x^2 - xy + 41y^2 with x and y nonnegative. - Jianing Song, Feb 19 2021

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005846, A202018.

Programs

Maple

select(p -> isprime(p) and (p=163 or numtheory:-legendre(-163,p)=1), [seq(2*i+1,i=1..1000)]);
# Another Maple program is given in A296920. - N. J. A. Sloane, Dec 25 2017

Mathematica

Reap[For[p=3, p<1000, p = NextPrime[p], If[p==163 || KroneckerSymbol[-163, p] == 1, Print[p]; Sow[p]]]][[2, 1]] (* Jean-François Alcover, Apr 29 2019 *)

PARI

is(n)=isprime(n) && issquare(Mod(-163,n)) \\ Charles R Greathouse IV, Nov 28 2016

Formula

a(n) ~ 2n log n. - Charles R Greathouse IV, Nov 28 2016