A332021 Elements of the set {m > 0: m is a quadratic nonresidue modulo prime(m)}.

2, 3, 6, 7, 8, 10, 11, 13, 15, 18, 21, 24, 26, 27, 28, 32, 33, 39, 41, 44, 45, 48, 50, 52, 54, 55, 56, 58, 60, 62, 65, 68, 69, 71, 74, 75, 79, 83, 84, 85, 88, 90, 93, 95, 101, 107, 108, 109, 110, 114, 116, 117, 118, 119, 120, 122, 123, 124, 126, 129, 130, 131, 133, 135, 139

Offset

1,1

Comments

This is the complement sequence of A332020.

The conjecture in A332020 implies that the number of terms not exceeding x is about x/2 asymptotically.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Example

a(1) = 2 since 2 is a quadratic nonresidue modulo prime(2) = 3.
a(2) = 3 since 3 is a quadratic nonresidue modulo prime(3) = 5.

Mathematica

tab = {}; Do[If[JacobiSymbol[n, Prime[n]] == -1, tab = Append[tab, n]], {n, 140}]; tab

Prog

(PARI) isok(m) = kronecker(m, prime(m)) !=1; \\ Michel Marcus, Feb 06 2020

Crossrefs

Cf. A000040, A000290, A242750, A332020.

Sequence in context: A299407 A028757 A184798 * A047560 A032899 A193528

Adjacent sequences: A332018 A332019 A332020 * A332022 A332023 A332024

Keyword

nonn

Author

Zhi-Wei Sun, Feb 04 2020

Status

approved