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A020649 Least quadratic nonresidue of n. 17
2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 5, 5, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 7, 2, 5, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 5, 2, 2, 5, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

a(n) is the smallest q such that the congruence x^2 == q (mod n) has no solution 0 < x < n, for n > 2. Note that a(n) is a prime. If n is an odd prime p, then a(p) is the smallest base b such that b^((p-1)/2) == -1 (mod p), see A053760. - Thomas Ordowski, Apr 24 2019

LINKS

Amiram Eldar, Table of n, a(n) for n = 3..10000

Eric Weisstein's World of Mathematics, Quadratic Nonresidue

FORMULA

a(prime(n)) = A053760(n) for n > 1. - Thomas Ordowski, Apr 24 2019

MATHEMATICA

a[n_] := Min @ Complement[Range[n - 1], Mod[Range[n/2]^2, n]]; Table[a[n], {n, 3, 110}] (* Amiram Eldar, Oct 29 2020 *)

PROG

(PARI) residue(n, m)={local(r); r=0; for(i=0, floor(m/2), if(i^2%m==n, r=1)); r}

A020649(n)={local(r, m); r=0; m=0; while(r==0, m=m+1; if(!residue(m, n), r=1)); m} \\ Michael B. Porter, Apr 30 2010

CROSSREFS

Cf. A053760.

Sequence in context: A231727 A270616 A304523 * A183024 A067131 A094915

Adjacent sequences:  A020646 A020647 A020648 * A020650 A020651 A020652

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified November 28 12:05 EST 2020. Contains 338720 sequences. (Running on oeis4.)