A296023 Numbers n such that there is precisely 1 group of order n and 2 of order n + 1.

3, 5, 13, 33, 37, 61, 73, 85, 133, 141, 145, 157, 177, 193, 213, 217, 277, 313, 345, 393, 397, 421, 445, 457, 481, 501, 537, 541, 553, 561, 565, 613, 661, 673, 697, 705, 717, 733, 745, 757, 793, 817, 865, 877, 885, 913, 933, 957, 973, 997, 1041, 1093, 1141, 1153

Offset: 1

Author

Muniru A Asiru, Dec 03 2017

Keywords

• nonn

Comments

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

Examples

			3 is in the sequence because 3 is a cyclic number and A000001(4) = 2. 5 is in the sequence because 5 is a cyclic number and A000001(6) = 2. Although 7 is a cyclic number, 7 is not in the sequence because A000001(8) = 5.
		

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..2000
• 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 cyclic numbers A003277.

Equals A373648 + 1.

Programs

GAP

A296023 := Filtered([1..2014], n -> [NumberSmallGroups(n), NumberSmallGroups(n+1)]=[1, 2]);

Maple

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

Formula

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