A298431 Numbers n such that there are precisely 14 groups of orders n and n + 1.

4328, 22311, 29864, 57896, 75368, 99368, 120807, 130664, 131943, 152295, 157287, 164072, 180327, 184232, 212456, 236583, 268712, 276392, 331112, 338792, 381927

Offset: 1

Author

Muniru A Asiru, Jan 19 2018

Keywords

• nonn
• more

Comments

Equivalently, lower member of consecutive terms of A294155.

Examples

			For n = 4328, A000001(4328) = A000001(4329) = 14.
For n = 22311, A000001(22311) = A000001(22312) = 14.
For n = 29864, A000001(29864) = A000001(29865) = 14.
		

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 A294155 (Numbers n having precisely 14 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), A298429 (k=12), A298430 (k=13), this sequence (k=14), A295995 (k=15).

Programs

Maple

with(GroupTheory): for n from 1 to 10^5 do if [NumGroups(n), NumGroups(n+1)] = [14, 14] then print(n); fi; od;

Formula

Sequence is { n | A000001(n) = 14, A000001(n+1) = 14 }.