A060649 Smallest number k==3 (mod 4) such that Q(sqrt(-k)) has class number n, or 0 if no such k exists.

3, 15, 23, 39, 47, 87, 71, 95, 199, 119, 167, 231, 191, 215, 239, 399, 383, 335, 311, 455, 431, 591, 647, 695, 479, 551, 983, 831, 887, 671, 719, 791, 839, 1079, 1031, 959, 1487, 1199, 1439, 1271, 1151, 1959, 1847, 1391, 1319, 2615, 3023, 1751, 1511, 1799

Offset: 1

Author

Robert G. Wilson v, Apr 17 2001

Keywords

• nonn

Comments

From Jianing Song, May 08 2021: (Start)

Conjecture 1: a(n) > 0 for all n;

Conjecture 2: a(n) = o(n^2). (End)

Conjecture: this is also the smallest absolute value of negative fundamental discriminant d for class number n. This is to say, for even n, if a(n) > 0 and A344072(n/2) > 0, then A344072(n/2) > a(n). - Jianing Song, Oct 03 2022

Links

• Jianing Song, Table of n, a(n) for n = 1..1162
• Eric Weisstein's World of Mathematics, Class Number.

Crossrefs

Cf. A002148, A081319, A344072, A038552.

Programs

Mathematica

(* First do <
				

PARI

a(n) = my(d=3); while(!isfundamental(-d) || qfbclassno(-d)!=n, d+=4); d \\ Jianing Song, May 08 2021

Extensions

Edited by Dean Hickerson, Mar 17 2003

Escape clause added by Jianing Song, May 08 2021