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A306224 a(n) is the smallest prime p such that -n is not a square mod p. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A282177 A184593 A249304 * A189202 A153098 A119280

Adjacent sequences:  A306221 A306222 A306223 * A306225 A306226 A306227

KEYWORD

nonn

AUTHOR

Jianing Song, Jan 30 2019

STATUS

approved

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Last modified September 21 19:59 EDT 2019. Contains 327282 sequences. (Running on oeis4.)