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A306493 a(n) is the least number such that the n-th prime is the least coprime quadratic nonresidue modulo a(n). 0
3, 4, 6, 22, 118, 479, 262, 3622, 5878, 18191, 24022, 132982, 296278, 366791, 1289738, 4539478, 6924458, 13620602, 32290442, 175244281, 86060762, 326769242, 131486759, 84286438, 937435558 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Different from A000229 because here the non-coprime quadratic nonresidues are ignored. For example, a(2) = 4 because although 2 is a quadratic nonresidue modulo 4, it is not coprime to 4.

LINKS

Table of n, a(n) for n=1..25.

EXAMPLE

For k = 118 we have: 2 is not coprime to 118, 11^2 == 3 (mod 118), 51^2 == 5 (mod 118), 19^2 == 7 (mod 118) and 11 is a quadratic nonresidue modulo 118. For all k < 118, at least one of 2, 3, 5, 7 is coprime quadratic nonresidue modulo k, so a(5) = 118.

PROG

(PARI) b(p, k) = gcd(p, k)==1&&!issquare(Mod(p, k))

a(n) = my(k=1); while(sum(i=1, n-1, b(prime(i), k))!=0 || !b(prime(n), k), k++); k

CROSSREFS

Cf. A000229.

Sequence in context: A038520 A294990 A081888 * A019209 A019120 A263940

Adjacent sequences:  A306490 A306491 A306492 * A306494 A306495 A306496

KEYWORD

nonn,more

AUTHOR

Jianing Song, Feb 19 2019

EXTENSIONS

a(17)-a(23) from Daniel Suteu, Feb 24 2019

a(24)-a(25) from Jinyuan Wang, Mar 08 2019

STATUS

approved

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Last modified August 11 12:12 EDT 2022. Contains 356065 sequences. (Running on oeis4.)