A298428 Numbers n such that there are precisely 10 groups of orders n and n + 1.

13914, 15974, 77234, 99126, 107205, 122675, 128894, 187473, 188265, 204134

Offset: 1

Author

Muniru A Asiru, Jan 19 2018

Keywords

• nonn
• more

Comments

Equivalently, lower member of consecutive terms of A249553.

Examples

			For n = 13914, A000001(13914) = A000001(13915) = 10.
For n = 15974, A000001(15974) = A000001(15975) = 10.
For n = 77234, A000001(77234) = A000001(77235) = 10.
		

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. Subsequence of A249553 (Numbers n having precisely 10 groups of order n). 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), this sequence (k=10), A295994 (k=11), A295995 (k=15).

Programs

Maple

with(GroupTheory): for n from 1 to 10^5 do if [NumGroups(n), NumGroups(n+1)] = [10, 10] then print(n); fi; od;

Formula

Sequence is { n | A000001(n) = 10, A000001(n+1) = 10 }.