A295993 - OEIS

%I #10 May 25 2019 01:37:02

%S 10845,32769,45837,47294

%N Numbers k such that there are precisely 8 groups of orders k and k + 1.

%C Equivalently, lower member of consecutive terms of A249551.

%C Other terms include 50225, 115785, 130974, 160474, 241366, 292774, 297689, 359106, 66885, 375254, 512974, 542654, 626354, 630002, 668205, 670074, 755825, 763637, 806518, 807274, 877162, 902565, 944414, but other terms may also be in this range. - _Robert Price_, May 24 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) = 8, A000001(n+1) = 8 }.

%e 10845 is in the sequence because A000001(10845) = A000001(10846) = 8, 32769 is in the sequence because A000001(32769) = A000001(32770) = 8 and 47294 is in the sequence because A000001(47294) = A000001(47295) = 8.

%t Select[Range[10^6], (FiniteGroupCount[#] == 8 && FiniteGroupCount[# + 1] == 8) &] (* A current limit in Mathematica is such that some orders >2047 may not be evaluated. *) (* _Robert Price_, May 24 2019 *)

%Y Cf. A000001, A249551.

%K nonn,more

%O 1,1

%A _Muniru A Asiru_, Dec 02 2017