A025021 Numbers whose least quadratic nonresidue (A020649) is 3.

7, 14, 17, 31, 34, 41, 49, 62, 79, 82, 89, 98, 103, 113, 119, 127, 137, 151, 158, 161, 178, 199, 206, 217, 223, 226, 233, 238, 254, 257, 271, 274, 281, 287, 289, 302, 322, 329, 343, 353, 367, 391, 398, 401, 434, 439, 446, 449, 463, 466, 487, 497, 511, 514, 521, 527, 542

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

n such that n is not divisible by 4, all primes dividing n are in A038873, and at least one prime dividing n is in A003630. - Robert Israel, Jul 19 2017

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Quadratic Nonresidue.

Crossrefs

Cf. A020649, A025020, A025022, A025023, A025024, A025025, A025026, A025027, A025028, A025029.

Cf. A003630, A038873.

Programs

Maple

select(t -> numtheory:-quadres(2,t) = 1 and numtheory:-quadres(3,t)=-1, [$1..1000]); # Robert Israel, Jul 19 2017

Mathematica

Select[Range[500], Min @ Complement[Range[# - 1], Mod[Range[#/2]^2, #]] == 3 &] (* Amiram Eldar, Oct 31 2020 *)

PARI

residue(n,m)={local(r);r=0;for(i=1,floor(m/2),if(i^2%m==n,r=1));r}
isA025021(n)=residue(2,n) && !residue(3,n) \\ Michael B. Porter, Apr 18 2010