A306493 a(n) is the least number such that the n-th prime is the least coprime quadratic nonresidue modulo a(n).

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

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