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

10845, 32769, 45837, 47294

Offset: 1

Author

Muniru A Asiru, Dec 02 2017

Keywords

• nonn
• more

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

Examples

			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.
		

Links

• 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

Crossrefs

Cf. A000001, A249551.

Programs

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 *)

Formula

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