A295990 Numbers n such that there are precisely 4 groups of orders n and n + 1.

315, 494, 603, 873, 1070, 1358, 1413, 1525, 1737, 1845, 1898, 1989, 2006, 2145, 2265, 2277, 2485, 2493, 2546, 2690, 2694, 2714, 2782, 3014, 3033, 3069, 3302, 3356, 3357, 3478, 3614, 3681, 3788, 3789, 4065, 4364, 4365, 4490, 4491, 4525, 4634, 4922, 4923, 4965, 5074, 5138, 5228, 5229

Offset: 1

Author

Muniru A Asiru, Dec 02 2017

Keywords

• nonn

Comments

Equivalently, lower member of consecutive terms of A054396.

Examples

			315 is in the sequence because A000001(315) = A000001(316) = 4, 494 is in the sequence because A000001(494) = A000001(495) = 4 and 2006 is in the sequence because A000001(2006) = A000001(2007) = 4.
		

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..448
• 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, A054396.

Programs

GAP

#A295990 := Filtered([1..2014], n -> [NumberSmallGroups(n), NumberSmallGroups(n+1)]=[4, 4]);

Formula

Sequence is { n | A000001(n) = 4, A000001(n+1) = 4 }.