A298429 Numbers n such that there are precisely 12 groups of orders n and n + 1.

30135, 76312, 130890, 173445, 356610

Offset: 1

Author

Muniru A Asiru, Jan 19 2018

Keywords

• nonn
• more

Comments

Equivalently, lower member of consecutive terms of A249555.

Examples

			For n = 30135, A000001(30135) = A000001(30136) = 12.
For n = 76312, A000001(76312) = A000001(76313) = 12.
For n = 130890, A000001(130890) = A000001(130891) = 12.
		

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 A249555 (Numbers n having precisely 12 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), A298428 (k=10), A295994 (k=11), this sequence (k=12), A298430 (k=13), A298431 (k=14), A295995 (k=15).

Programs

Maple

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

Formula

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