A296024 Numbers n such that there is precisely 1 group of order n, 2 of order n + 1 and 3 of order n + 2.

73, 865, 2065, 2173, 3973, 7933, 10333, 12633, 15121, 16537, 17473, 19237, 20317, 20337, 20665, 23773, 23881, 24421, 25093, 28921, 31477, 33133, 35137, 36877, 38173, 41017, 41773, 42061, 46021

Offset: 1

Author

Muniru A Asiru, Dec 03 2017

Keywords

• nonn

Comments

Equivalently, lower member of consecutive terms of A296023.

Being a subsequence of A003277, all the terms are odd.

Examples

			73 is in the sequence because 73 is a cyclic number, A000001(74) = 2 and A000001(75) = 3.
865 is in the sequence because 865 is a cyclic number, A000001(866) = 2 and A000001(867) = 3.
20317 is in the sequence because 20317 is a cyclic number, A000001(20318) = 2 and A000001(20319) = 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, A003277. Subsequence of A296023.

Equals A373649 + 1.

Programs

Maple

with(GroupTheory): with(numtheory):
for n from 1 to 10^5 do if [NumGroups(n), NumGroups(n+1), NumGroups(n+2)]=[1, 2, 3]  then print(n); fi; od;

Formula

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