A298912 Numbers n such that the number of groups of order n equals the number of groups of order n + 1.

1, 2, 9, 21, 25, 38, 45, 57, 93, 105, 121, 165, 194, 201, 202, 205, 206, 218, 253, 261, 301, 315, 325, 326, 357, 361, 381, 385, 422, 453, 477, 482, 494, 506, 538, 542, 554, 603, 614, 626, 633, 662, 746, 758, 765, 801, 841, 861, 873, 897, 921, 925, 934, 1005, 1017

Offset: 1

Author

Muniru A Asiru, Jan 28 2018

Keywords

• nonn

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
• Index entries for sequences related to groups

Crossrefs

Cf. A000001. Numbers n having precisely k groups of orders n and n + 1: A295230 (k=2), A295990 (k=4), A295991 (k=5), A295992 (k=6), A295993 (k=8), A298427 (k=9), A (k=10), A295994 (k=11), A295995 (k=15).

Programs

GAP

Filtered([1..500], n -> NumberSmallGroups(n) = NumberSmallGroups(n+1));

Maple

with(GroupTheory):
for n from 1 to 300 do if NumGroups(n+1) = NumGroups(n) then print(n); fi; od;

Formula

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