A298427 Numbers n such that there are precisely 9 groups of orders n and n + 1.

38227, 113476, 155827, 269444, 336931, 411747

Offset: 1

Author

Muniru A Asiru, Jan 19 2018

Keywords

• nonn
• more

Comments

Equivalently, lower member of consecutive terms of A249552.

Examples

			For n = 38227, A000001(38227) = A000001(38228) = 9.
For n = 113476, A000001(113476) = A000001(113477) = 9.
For n = 155827, A000001(155827) = A000001(155828) = 9.
		

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 A249552 (Numbers n having precisely 9 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), this sequence (k=9), A298428 (k=10), A295994 (k=11), A295995 (k=15).

Programs

Maple

with(GroupTheory): for n from 1 to 10^6 do if [NumGroups(n), NumGroups(n+1)] = [9, 9] then print(n); fi; od;

Formula

Sequence is { n | [A000001(n), A000001(n+1)] = [9, 9] }.