A295993 Numbers k such that there are precisely 8 groups of orders k and k + 1.

10845, 32769, 45837, 47294

Offset

1,1

Comments

Equivalently, lower member of consecutive terms of A249551.

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

Links

Table of n, a(n) for n=1..4.

H. U. Besche, B. Eick and E. A. O'Brien. A Millennium Project: Constructing Small Groups, Internat. J. Algebra and Computation, 12 (2002), 623-644.

Gordon Royle, Numbers of Small Groups

Index entries for sequences related to groups

Formula

Sequence is { n | A000001(n) = 8, A000001(n+1) = 8 }.

Example

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.

Mathematica

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 *)

Crossrefs

Cf. A000001, A249551.

Sequence in context: A237190 A065321 A252064 * A185517 A250954 A334003

Adjacent sequences: A295990 A295991 A295992 * A295994 A295995 A295996

Keyword

nonn,more

Author

Muniru A Asiru, Dec 02 2017

Status

approved