A355876 Smallest prime p == 1 (mod 8) such that Q(sqrt(p)) has class number 2n+1.

17, 257, 401, 577, 1129, 1297, 13033, 11321, 11257, 38569, 7057, 23593, 27689, 8761, 56857, 284561, 63361, 25601, 24337, 55441, 458929, 14401, 32401, 78401, 70969, 69697, 376897, 106537, 41617, 160001, 193601, 57601, 197137, 367721, 414433, 1506473, 444089, 331777, 156817

Offset: 0

Author

Jianing Song, Jul 20 2022

Keywords

• nonn

Comments

It seems that a(n) < A355877(n) for most n. a(n) > A355877(n) for n = 0, 1, 6, 9, 15, 20, 35, ...

Examples

			p = 257 is the smallest prime congruent to 1 modulo 8 such that Q(sqrt(p)) has class number 3, so a(1) = 257.
		

Links

• Jianing Song, Table of n, a(n) for n = 0..57
• Wikipedia, Class numbers of quadratic fields
• Index entries for sequences related to quadratic fields

Crossrefs

Cf. A355878.

Similar sequences: A002148 (p == 3 (mod 8)), A355877 (p == 5 (mod 8)), A002146 (p == 7 (mod 8)).

Programs

PARI

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