A355877 -id:A355877 - cp's OEIS frontend

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

Jianing Song, Jul 20 2022

nonn

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

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

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

Cf. A355878.

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

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

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

Original entry on oeis.org

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

Jianing Song, Jul 20 2022

nonn

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.

			p = 229 is the smallest odd prime such that Q(sqrt(p)) has class number 3, so a(1) = 229.

Cf. A355876, A355877.

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

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

cp's OEIS Frontend

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

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