A295230 Numbers n such that there are precisely 2 groups of orders n and n + 1.

9, 21, 25, 38, 45, 57, 93, 105, 121, 165, 194, 201, 202, 205, 206, 218, 253, 261, 301, 325, 326, 357, 361, 381, 385, 422, 453, 477, 482, 538, 542, 554, 614, 626, 633, 662, 746, 758, 765, 801, 841, 861, 897, 921, 925, 934, 1005, 1017, 1045, 1046, 1081, 1094, 1113, 1126, 1137

Offset: 1

Author

Muniru A Asiru, Nov 18 2017

Keywords

• nonn

Comments

Equivalently, lower member of consecutive terms of A054395.

Examples

			9 is in the sequence because A000001(9) = A000001(10) = 2, 21 is in the sequence because A000001(21) = A000001(22) = 2 and 325 is in the sequence because A000001(325) = A000001(326) = 2. - _Muniru A Asiru_, Dec 02 2017
		

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..1415
• 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, A054395.

Programs

GAP

A295230 := Filtered([1..2014], n -> [NumberSmallGroups(n), NumberSmallGroups(n+1)]=[2, 2]);

Mathematica

Select[Range[1200], FiniteGroupCount[#] == 2 && FiniteGroupCount[# + 1] == 2 &] (* Jean-François Alcover, Dec 08 2017 *)
SequencePosition[FiniteGroupCount[Range[1200]],{2,2}][[;;,1]] (* Harvey P. Dale, Aug 18 2023 *)

Formula

Sequence is { n | A000001(n) = 2, A000001(n+1) = 2 }.