cp's OEIS Frontend

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

%I A296023 #21 Jul 04 2024 16:14:01
%S A296023 3,5,13,33,37,61,73,85,133,141,145,157,177,193,213,217,277,313,345,
%T A296023 393,397,421,445,457,481,501,537,541,553,561,565,613,661,673,697,705,
%U A296023 717,733,745,757,793,817,865,877,885,913,933,957,973,997,1041,1093,1141,1153
%N A296023 Numbers n such that there is precisely 1 group of order n and 2 of order n + 1.
%C A296023 Being a subsequence of A003277, all the terms are odd.
%H A296023 Muniru A Asiru, <a href="/A296023/b296023.txt">Table of n, a(n) for n = 1..2000</a>
%H A296023 H. U. Besche, B. Eick and E. A. O'Brien, <a href="http://dx.doi.org/10.1142/S0218196702001115">A Millennium Project: Constructing Small Groups</a>, Internat. J. Algebra and Computation, 12 (2002), 623-644.
%H A296023 Gordon Royle, <a href="http://staffhome.ecm.uwa.edu.au/~00013890/remote/cubcay/">Numbers of Small Groups</a>
%H A296023 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%F A296023 Sequence is { n | A000001(n) = 1, A000001(n+1) = 2 }.
%e A296023 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.
%p A296023 with(GroupTheory): with(numtheory):
%p A296023 for n from 1 to 10^3 do if [NumGroups(n),NumGroups(n+1)]=[1, 2]  then print(n); fi; od;
%o A296023 (GAP) A296023 := Filtered([1..2014], n -> [NumberSmallGroups(n), NumberSmallGroups(n+1)]=[1, 2]);
%Y A296023 Cf. A000001. Subsequence of cyclic numbers A003277.
%Y A296023 Equals A373648 + 1.
%K A296023 nonn
%O A296023 1,1
%A A296023 _Muniru A Asiru_, Dec 03 2017