A357573 Largest even k such that h(-k) = 2n, where h(D) is the class number of the quadratic field with discriminant D; or 0 if no such k exists.

232, 1012, 1588, 3448, 5272, 8248, 9172, 14008, 21652, 21508, 26548, 32008, 45208, 53188, 57688, 65668, 73588, 85012, 121972, 120712, 117748, 137272, 189352, 162628, 174868, 201268, 194968, 249208, 188248, 332872, 341608, 424708, 370792, 411832, 377512, 539092, 332308, 486088, 369832, 435268, 604948, 667192, 548788, 601528, 596212, 566008, 737752, 795832, 645208, 802888

Offset

1,1

Comments

By definition, a(n) <= 4*A038552(2n).

Conjecture: if A038552(2n) == 3 (mod 4), a(n) > 0, then a(n) < A038552(2n). If this is true, then A038552(n) is also the largest absolute value of negative fundamental discriminant d for class number n.

Conjecture: every term is congruent 4 or 16 (mod 24). Ralf Stephan, May 23 2026

Links

Table of n, a(n) for n=1..50.

Example

a(1) = 232: h(-k) = 2 <=> k = 15, 20, 24, 35, 40, 51, 52, 88, 91, 115, 123, 148, 187, 232, 235, 267, 403, 427, so the largest even k such that h(-k) = 2 is k = 232.

Crossrefs

Cf. A038552, A344072.

Sequence in context: A252273 A153466 A200870 * A234690 A234683 A366816

Adjacent sequences: A357570 A357571 A357572 * A357574 A357575 A357576

Keyword

nonn,hard

Author

Jianing Song, Oct 03 2022

Status

approved