cp's OEIS Frontend

A296022 Numbers n such that there are precisely 2 groups of orders n, n + 1 and n + 2.

%I A296022 #22 Jan 28 2018 18:57:43
%S A296022 201,205,325,1045,1653,1857,1965,2041,2301,2305,2605,2637,2653,2853,
%T A296022 2973,3241,3445,3505,3721,3757,4173,4405,4585,4693,5005,5217,5241,
%U A296022 5341,5685,5757,5853,6685,6745,7285,8005,8845,9325,9441,9777,10201,10293,10417,10833
%N A296022 Numbers n such that there are precisely 2 groups of orders n, n + 1 and n + 2.
%C A296022 Equivalently, lower member of consecutive terms of A295230.
%H A296022 Muniru A Asiru, <a href="/A296022/b296022.txt">Table of n, a(n) for n = 1..2583</a>
%H A296022 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 A296022 Gordon Royle, <a href="http://staffhome.ecm.uwa.edu.au/~00013890/remote/cubcay/">Numbers of Small Groups</a>
%H A296022 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%F A296022 Sequence is { n | A000001(n) = 2, A000001(n+1) = 2, A000001(n+2) = 2 }.
%e A296022 n = 201 -> A000001(201) = A000001(202) = A000001(203) = 2.
%e A296022 n = 205 -> A000001(205) = A000001(206) = A000001(207) = 2.
%e A296022 n = 1965 -> A000001(1965) = A000001(1966) = A000001(1967) = 2.
%p A296022 with(GroupTheory): with(numtheory):
%p A296022 for n from 1 to 10^4 do if [NumGroups(n),NumGroups(n+1),NumGroups(n+2)]=[2,2,2]  then print(n); fi; od;
%t A296022 cnt = FiniteGroupCount; Select[Range[10^4], cnt[#] == cnt[#+1] == cnt[#+2] == 2&] (* _Jean-François Alcover_, Dec 08 2017 *)
%o A296022 (GAP) A296022 := Filtered([1..2013], n -> [NumberSmallGroups(n), NumberSmallGroups(n+1), NumberSmallGroups(n+2)]=[2, 2, 2]);
%Y A296022 Cf. A000001, A054396. Subsequence of A295230.
%K A296022 nonn
%O A296022 1,1
%A A296022 _Muniru A Asiru_, Dec 03 2017