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

1,1

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.

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 *)

Prog

(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

Crossrefs

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

Cf. A003630, A038873.

Sequence in context: A092433 A056203 A178732 * A326767 A131439 A213604

Adjacent sequences: A025018 A025019 A025020 * A025022 A025023 A025024

Keyword

nonn

Author

David W. Wilson

Status

approved