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A295230 Numbers n such that there are precisely 2 groups of orders n and n + 1.

%I A295230 #20 Aug 18 2023 11:34:47
%S A295230 9,21,25,38,45,57,93,105,121,165,194,201,202,205,206,218,253,261,301,
%T A295230 325,326,357,361,381,385,422,453,477,482,538,542,554,614,626,633,662,
%U A295230 746,758,765,801,841,861,897,921,925,934,1005,1017,1045,1046,1081,1094,1113,1126,1137
%N A295230 Numbers n such that there are precisely 2 groups of orders n and n + 1.
%C A295230 Equivalently, lower member of consecutive terms of A054395.
%H A295230 Muniru A Asiru, <a href="/A295230/b295230.txt">Table of n, a(n) for n = 1..1415</a>
%H A295230 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 A295230 Gordon Royle, <a href="http://staffhome.ecm.uwa.edu.au/~00013890/remote/cubcay/">Numbers of Small Groups</a>
%H A295230 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%F A295230 Sequence is { n | A000001(n) = 2, A000001(n+1) = 2 }.
%e A295230 9 is in the sequence because A000001(9) = A000001(10) = 2, 21 is in the sequence because A000001(21) = A000001(22) = 2 and 325 is in the sequence because A000001(325) = A000001(326) = 2. - _Muniru A Asiru_, Dec 02 2017
%t A295230 Select[Range[1200], FiniteGroupCount[#] == 2 && FiniteGroupCount[# + 1] == 2 &] (* _Jean-François Alcover_, Dec 08 2017 *)
%t A295230 SequencePosition[FiniteGroupCount[Range[1200]],{2,2}][[;;,1]] (* _Harvey P. Dale_, Aug 18 2023 *)
%o A295230 (GAP) A295230 := Filtered([1..2014], n -> [NumberSmallGroups(n), NumberSmallGroups(n+1)]=[2, 2]);
%Y A295230 Cf. A000001, A054395.
%K A295230 nonn
%O A295230 1,1
%A A295230 _Muniru A Asiru_, Nov 18 2017