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%I #6 Jan 28 2018 13:45:44
%S 83132,86049,173529,492830,704241,889406
%N Numbers n such that there are precisely 16 groups of orders n and n + 1.
%C Equivalently, lower member of consecutive terms of A295161.
%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) = 16, A000001(n+1) = 16 }.
%e For n = 83132, A000001(83132) = A000001(83133) = 16.
%e For n = 173529, A000001(173529) = A000001(173530) = 16.
%e For n = 492830, A000001(492830) = A000001(492831) = 16.
%p with(GroupTheory): for n from 1 to 10^6 do if [NumGroups(n), NumGroups(n+1)] = [16, 16] then print(n); fi; od;
%Y Cf. A000001. Subsequence of A295161 (Numbers n having precisely 16 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), A298427 (k=9), A298428 (k=10), A295994 (k=11), A298429 (k=12), A298430 (k=13), A298431 (k=14), A295995 (k=15), this sequence (k=16).
%K nonn,more
%O 1,1
%A _Muniru A Asiru_, Jan 19 2018
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