A296022 Numbers n such that there are precisely 2 groups of orders n, n + 1 and n + 2.

201, 205, 325, 1045, 1653, 1857, 1965, 2041, 2301, 2305, 2605, 2637, 2653, 2853, 2973, 3241, 3445, 3505, 3721, 3757, 4173, 4405, 4585, 4693, 5005, 5217, 5241, 5341, 5685, 5757, 5853, 6685, 6745, 7285, 8005, 8845, 9325, 9441, 9777, 10201, 10293, 10417, 10833

Offset: 1

Author

Muniru A Asiru, Dec 03 2017

Keywords

• nonn

Comments

Equivalently, lower member of consecutive terms of A295230.

Examples

			n = 201 -> A000001(201) = A000001(202) = A000001(203) = 2.
n = 205 -> A000001(205) = A000001(206) = A000001(207) = 2.
n = 1965 -> A000001(1965) = A000001(1966) = A000001(1967) = 2.
		

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..2583
• 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. Subsequence of A295230.

Programs

GAP

A296022 := Filtered([1..2013], n -> [NumberSmallGroups(n), NumberSmallGroups(n+1), NumberSmallGroups(n+2)]=[2, 2, 2]);

Maple

with(GroupTheory): with(numtheory):
for n from 1 to 10^4 do if [NumGroups(n),NumGroups(n+1),NumGroups(n+2)]=[2,2,2]  then print(n); fi; od;

Mathematica

cnt = FiniteGroupCount; Select[Range[10^4], cnt[#] == cnt[#+1] == cnt[#+2] == 2&] (* Jean-François Alcover, Dec 08 2017 *)

Formula

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