A298427 - OEIS

%I #11 Jan 28 2018 13:44:51

%S 38227,113476,155827,269444,336931,411747

%N Numbers n such that there are precisely 9 groups of orders n and n + 1.

%C Equivalently, lower member of consecutive terms of A249552.

%H 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 Gordon Royle, <a href="http://staffhome.ecm.uwa.edu.au/~00013890/remote/cubcay/">Numbers of Small Groups</a>

%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>

%F Sequence is { n | [A000001(n), A000001(n+1)] = [9, 9] }.

%e For n = 38227, A000001(38227) = A000001(38228) = 9.

%e For n = 113476, A000001(113476) = A000001(113477) = 9.

%e For n = 155827, A000001(155827) = A000001(155828) = 9.

%p with(GroupTheory): for n from 1 to 10^6 do if [NumGroups(n), NumGroups(n+1)] = [9, 9] then print(n); fi; od;

%Y Cf. A000001. Subsequence of A249552 (Numbers n having precisely 9 groups of order n). Numbers n having precisely k groups of orders n and n+1: A295230 (k=2), A295990 (k=4), A295991 (k=5), A295992 (k=6), A295993 (k=8), this sequence (k=9), A298428 (k=10), A295994 (k=11), A295995 (k=15).

%K nonn,more

%O 1,1

%A _Muniru A Asiru_, Jan 19 2018