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A298429
Numbers k such that there are precisely 12 groups of order k and precisely 12 of order k + 1.
3
30135, 76312, 130890, 173445, 356610
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
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]
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
KEYWORD
nonn,more
AUTHOR
Muniru A Asiru, Jan 19 2018
STATUS
approved