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A060649 Smallest number k==3 (mod 4) such that Q(sqrt(-k)) has class number n, or 0 if no such k exists. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

From Jianing Song, May 08 2021: (Start)

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

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

LINKS

Jianing Song, Table of n, a(n) for n = 1..1162

Eric Weisstein's World of Mathematics, Class Number.

MATHEMATICA

(* First do <<NumberTheory`NumberTheoryFunctions` *) a=Table[0, {50}]; Do[If[SquareFreeQ[n], c=ClassNumber[ -n]; If[c<=50&&a[[c]]==0, a[[c]]=n]], {n, 3, 3200, 4}]; a

PROG

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

CROSSREFS

Cf. A002148, A081319.

Sequence in context: A106403 A225365 A225060 * A344073 A009210 A142882

Adjacent sequences:  A060646 A060647 A060648 * A060650 A060651 A060652

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Apr 17 2001

EXTENSIONS

Edited by Dean Hickerson, Mar 17 2003

Escape clause added by Jianing Song, May 08 2021

STATUS

approved

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Last modified May 28 18:07 EDT 2022. Contains 354120 sequences. (Running on oeis4.)