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

1,1

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.

Links

Table of n, a(n) for n=1..87.

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).

Prog

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

Crossrefs

Cf. A144294.

See A306220 for another version.

Sequence in context: A328154 A249304 A333906 * A189202 A153098 A329509

Adjacent sequences: A306221 A306222 A306223 * A306225 A306226 A306227

Keyword

nonn

Author

Jianing Song, Jan 30 2019

Status

approved