A355878 -id:A355878 - 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)))

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

Original entry on oeis.org

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

Jianing Song, Jul 20 2022

nonn

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

Cf. A355878.

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

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

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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