A298429 - OEIS

A298429

Numbers k such that there are precisely 12 groups of order k and precisely 12 of order k + 1.

30135, 76312, 130890, 173445, 356610

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Equivalently, lower member of consecutive terms of A249555.

There are currently serious doubts about the correctness of the terms generated with Maple, starting with a(2). Until this is clarified, this sequence should be considered potentially erroneous. - Hugo Pfoertner, Feb 28 2026

LINKS

Table of n, a(n) for n=1..5.

H. U. Besche, B. Eick and E. A. O'Brien, A Millennium Project: Constructing Small Groups, Internat. J. Algebra and Computation, 12 (2002), 623-644.

Gordon Royle, Numbers of Small Groups [broken link]

Index entries for sequences related to groups

FORMULA

Sequence is { n | A000001(n) = 12, A000001(n+1) = 12 }.

EXAMPLE

For k = 30135, A000001(30135) = A000001(30136) = 12.

For k = 76312, A000001(76312) = A000001(76313) = 12.

For k = 130890, A000001(130890) = A000001(130891) = 12.

MAPLE

with(GroupTheory): for n from 1 to 10^6 do if [NumGroups(n), NumGroups(n+1)] = [12, 12] then print(n); fi; od;

CROSSREFS

Cf. A000001. Subsequence of A249555 (Numbers k having precisely 12 groups of order k). Numbers m having precisely k groups of orders m and m+1: A295230 (k=2), A295990 (k=4), A295991 (k=5), A295992 (k=6), A295993 (k=8), A298427 (k=9), A298428 (k=10), A295994 (k=11), this sequence (k=12), A298430 (k=13), A298431 (k=14), A295995 (k=15).

Sequence in context: A027665 A260459 A202598 * A255759 A255752 A254841

Adjacent sequences: A298426 A298427 A298428 * A298430 A298431 A298432

KEYWORD

nonn,more

AUTHOR

Muniru A Asiru, Jan 19 2018

STATUS

approved