A355878 Smallest p == 1 (mod 4) such that Q(sqrt(p)) has class number 2n+1.

5, 229, 401, 577, 1129, 1297, 8101, 11321, 11257, 18229, 7057, 23593, 27689, 8761, 56857, 146077, 63361, 25601, 24337, 55441, 439573, 14401, 32401, 78401, 70969, 69697, 376897, 106537, 41617, 160001, 193601, 57601, 197137, 367721, 414433, 1432813, 444089, 331777

Offset: 0

Author

Jianing Song, Jul 20 2022

Keywords

• nonn

Comments

Also smallest odd prime p such that Q(sqrt(p)) has narrow class number (also called form class number) 2n+1.

Conjecture: a(n) > A002148(n) for all n.

Examples

			p = 229 is the smallest odd prime 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. A355876, A355877.

Programs

PARI

a(n) = forprime(p=2, oo, if(p%4==1 && qfbclassno(p)==2*n+1, return(p)))

Formula

a(n) = min(A355876(n),A355877(n)).