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%I #13 May 24 2019 16:39:26
%S 506,4718,6909,32474,32585,39225,46598,47937
%N Numbers k such that there are precisely 6 groups of orders k and k + 1.
%C Equivalently, lower member of consecutive terms of A135850.
%C Other terms in this sequence are: 51009, 75525, 86174, 95109, 96837, 118202, 123057, 126825, 134210, 139209, 143142, 148910, 157322, 169197, 218517, 249710, 261674, 262274, 271778, 273825, 297609, 300909, 310497, 379274, 391910, 449709, 501105, 511574, 526274, 538425, 552146, 559041, 570506, 582658, 588146, 589910, 596210, 629210, 639302, 648654, 650274, 653174, 658574, 658734, 668210, 668409, 680225, 697454, 742274, 753909, 768009, 810122, 823305, 847310, 854510, 870110, 891225, 928010, 935325, 952574, 960621, 964725, 978873, 981573, 983025. There are probably others in this range. - _Robert Price_, May 23 2019
%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) = 6, A000001(n+1) = 6 }.
%e 506 is in the sequence because A000001(506) = A000001(507) = 6, 4718 is in the sequence because A000001(4718) = A000001(4719) = 6 and 32585 is in the sequence because A000001(32585) = A000001(32586) = 6.
%t Select[Range[10^6], (FiniteGroupCount[#] == 6 && FiniteGroupCount[# + 1] == 6) &] (* Due to a limit in Mathematica, some numbers >2047 cannot be evaluated. *) (* _Robert Price_, May 23 2019 *)
%Y Cf. A000001, A135850.
%K nonn,more
%O 1,1
%A _Muniru A Asiru_, Dec 02 2017
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