A306224 a(n) is the smallest prime p such that -n is not a square mod p.

3, 5, 5, 3, 11, 13, 3, 5, 7, 3, 7, 5, 3, 11, 7, 3, 5, 5, 3, 11, 13, 3, 5, 13, 3, 11, 5, 3, 7, 7, 3, 5, 5, 3, 19, 7, 3, 5, 7, 3, 13, 5, 3, 7, 11, 3, 5, 5, 3, 7, 7, 3, 5, 13, 3, 11, 5, 3, 11, 7, 3, 5, 5, 3, 7, 19, 3, 5, 11, 3, 7, 5, 3, 7, 11, 3, 5, 5, 3, 11, 7, 3, 5, 13, 3, 7, 5

Offset: 1

Author

Jianing Song, Jan 30 2019

Keywords

• nonn

Comments

a(n) is the smallest odd prime p such that Kronecker(-n,p) = -1.

A companion sequence to A144294.

Conjecture: lim sup log(a(n))/log(n) = 0.

Crossrefs

Cf. A144294.

See A306220 for another version.

Programs

PARI

a(n) = forprime(p=3, , if(kronecker(-n, p)<0, return(p)))

Formula

a(n) = 3 if and only if n == 1 (mod 3).

a(n) = 5 if and only if n == 2, 3, 8, 12 (mod 15).