A296025 Numbers n such that there are precisely 2 groups of order n and 3 of order n + 1.

74, 362, 866, 2066, 2174, 3974, 4894, 5042, 5914, 6626, 7934, 10334, 10886, 12634, 15122, 16538, 17474, 19238, 20318, 20338, 20666, 21974, 23774, 23882, 24422, 25094, 28922, 31478, 33134, 35138, 36878, 38174, 41018, 41774, 42062, 42134, 46022, 48502

Offset: 1

Author

Muniru A Asiru, Dec 03 2017

Keywords

• nonn

Examples

			74 is in the sequence since A000001(74) = 2 and A000001(75) = 3.
362 is in the sequence since A000001(362) = 2 and A000001(363) = 3.
7934 is in the sequence since A000001(7934) = 2 and A000001(7935) = 3.
		

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 A054395.

Programs

Maple

with(GroupTheory): with(numtheory):
for n from 1 to 10^4 do if [NumGroups(n), NumGroups(n+1)]=[2, 3] then print(n); fi; od;

Formula

Sequence is { n | A000001(n) = 2, A000001(n+1) = 3 }.