cp's OEIS Frontend

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

%I A296024 #21 Jul 04 2024 16:17:35
%S A296024 73,865,2065,2173,3973,7933,10333,12633,15121,16537,17473,19237,20317,
%T A296024 20337,20665,23773,23881,24421,25093,28921,31477,33133,35137,36877,
%U A296024 38173,41017,41773,42061,46021
%N A296024 Numbers n such that there is precisely 1 group of order n, 2 of order n + 1 and 3 of order n + 2.
%C A296024 Equivalently, lower member of consecutive terms of A296023.
%C A296024 Being a subsequence of A003277, all the terms are odd.
%H A296024 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 A296024 Gordon Royle, <a href="http://staffhome.ecm.uwa.edu.au/~00013890/remote/cubcay/">Numbers of Small Groups</a>
%H A296024 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%F A296024 Sequence is { n | A000001(n) = 1, A000001(n+1) = 2, A000001(n+2) = 3 }.
%e A296024 73 is in the sequence because 73 is a cyclic number, A000001(74) = 2 and A000001(75) = 3.
%e A296024 865 is in the sequence because 865 is a cyclic number, A000001(866) = 2 and A000001(867) = 3.
%e A296024 20317 is in the sequence because 20317 is a cyclic number, A000001(20318) = 2 and A000001(20319) = 3.
%p A296024 with(GroupTheory): with(numtheory):
%p A296024 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;
%Y A296024 Cf. A000001, A003277. Subsequence of A296023.
%Y A296024 Equals A373649 + 1.
%K A296024 nonn
%O A296024 1,1
%A A296024 _Muniru A Asiru_, Dec 03 2017