cp's OEIS Frontend

A296026 Numbers n such that there are precisely 2 groups of order n and 4 of order n + 1.

%I A296026 #14 Jan 28 2018 18:57:31
%S A296026 62,129,153,169,237,245,274,278,285,289,314,369,386,417,425,429,497,
%T A296026 529,555,597,637,645,669,715,813,889,914,926,955,961,969,1065,1101,
%U A296026 1131,1154,1221,1227,1286,1341,1369,1389,1405,1435,1461,1497,1505,1515,1557,1569,1675,1771
%N A296026 Numbers n such that there are precisely 2 groups of order n and 4 of order n + 1.
%H A296026 Muniru A Asiru, <a href="/A296026/b296026.txt">Table of n, a(n) for n = 1..1241</a>
%H A296026 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 A296026 Gordon Royle, <a href="http://staffhome.ecm.uwa.edu.au/~00013890/remote/cubcay/">Numbers of Small Groups</a>
%H A296026 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%F A296026 Sequence is { n | A000001(n) = 2, A000001(n+1) = 4 }.
%e A296026 62 is in the sequence since A000001(62) = 2 and A000001(63) = 4.
%e A296026 129 is in the sequence since A000001(129) = 2 and A000001(130) = 4.
%e A296026 425 is in the sequence since A000001(425) = 2 and A000001(426) = 4.
%p A296026 with(GroupTheory):
%p A296026 for n from 1 to 10^3 do if [NumGroups(n), NumGroups(n+1)]=[2, 4]  then print(n); fi; od;
%o A296026 (GAP) A296026 := Filtered([1..2014],n->[NumberSmallGroups(n), NumberSmallGroups(n+1)]=[2, 4]);
%Y A296026 Cf. A000001. Subsequence of A054395.
%K A296026 nonn
%O A296026 1,1
%A A296026 _Muniru A Asiru_, Dec 03 2017