A295990 - OEIS

%I #11 Dec 06 2017 04:57:07

%S 315,494,603,873,1070,1358,1413,1525,1737,1845,1898,1989,2006,2145,

%T 2265,2277,2485,2493,2546,2690,2694,2714,2782,3014,3033,3069,3302,

%U 3356,3357,3478,3614,3681,3788,3789,4065,4364,4365,4490,4491,4525,4634,4922,4923,4965,5074,5138,5228,5229

%N Numbers n such that there are precisely 4 groups of orders n and n + 1.

%C Equivalently, lower member of consecutive terms of A054396.

%H Muniru A Asiru, <a href="/A295990/b295990.txt">Table of n, a(n) for n = 1..448</a>

%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) = 4, A000001(n+1) = 4 }.

%e 315 is in the sequence because A000001(315) = A000001(316) = 4, 494 is in the sequence because A000001(494) = A000001(495) = 4 and 2006 is in the sequence because A000001(2006) = A000001(2007) = 4.

%o (GAP) #A295990 := Filtered([1..2014], n -> [NumberSmallGroups(n), NumberSmallGroups(n+1)]=[4, 4]);

%Y Cf. A000001, A054396.

%K nonn

%O 1,1

%A _Muniru A Asiru_, Dec 02 2017