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Odd primes modulo which -163 is a square.
4

%I #20 Feb 20 2021 00:47:32

%S 41,43,47,53,61,71,83,97,113,131,151,163,167,173,179,197,199,223,227,

%T 251,263,281,307,313,347,359,367,373,379,383,397,409,419,421,439,457,

%U 461,487,499,503,523,547,563,577,593,607,641,647,653,661,673,677,691

%N Odd primes modulo which -163 is a square.

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

%C Primes that divide some member of A202018.

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

%C 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

%H Robert Israel, <a href="/A257362/b257362.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) ~ 2n log n. - _Charles R Greathouse IV_, Nov 28 2016

%p select(p -> isprime(p) and (p=163 or numtheory:-legendre(-163,p)=1), [seq(2*i+1,i=1..1000)]);

%p # Another Maple program is given in A296920. - _N. J. A. Sloane_, Dec 25 2017

%t 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 *)

%o (PARI) is(n)=isprime(n) && issquare(Mod(-163,n)) \\ _Charles R Greathouse IV_, Nov 28 2016

%Y Cf. A005846, A202018.

%K nonn,easy

%O 1,1

%A _Robert Israel_, Apr 20 2015