A355877 Smallest prime p == 5 (mod 8) such that Q(sqrt(p)) has class number 2n+1.

5, 229, 1093, 2029, 7573, 12589, 8101, 13693, 54541, 18229, 75629, 91813, 59053, 65029, 72901, 146077, 127453, 199813, 169909, 209581, 439573, 189229, 197341, 324901, 378229, 596293, 430861, 352837, 712981, 1137229, 700573, 245029, 574261, 770533, 860701, 1432813, 1821877, 1092829

Offset: 0

Author

Jianing Song, Jul 20 2022

Keywords

• nonn

Examples

			p = 229 is the smallest prime congruent to 5 modulo 8 such that Q(sqrt(p)) has class number 3, so a(1) = 229.
		

Links

• Wikipedia, Class numbers of quadratic fields
• Index entries for sequences related to quadratic fields

Crossrefs

Cf. A355878.

Similar sequences: A355876 (p == 1 (mod 8)), A002148 (p == 3 (mod 8)), A002146 (p == 7 (mod 8)).

Programs

PARI

a(n) = forprime(p=2, oo, if(p%8==5 && qfbclassno(p)==2*n+1, return(p)))