cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A005180 Orders of simple groups.

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%I A005180 M0651 #35 Jun 15 2024 17:58:20
%S A005180 1,2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,60,61,67,71,73,79,
%T A005180 83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,168,
%U A005180 173,179,181,191,193,197,199,211,223,227,229,233,239,241
%N A005180 Orders of simple groups.
%C A005180 Officially the group of order 1 is not considered to be simple - see for example Rotman, Group Theory.
%D A005180 J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites].
%D A005180 M. Hall, Jr., A search for simple groups of order less than one million, pp. 137-168 of J. Leech, editor, Computational Problems in Abstract Algebra. Pergamon, Oxford, 1970.
%D A005180 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005180 T. D. Noe, <a href="/A005180/b005180.txt">Table of n, a(n) for n = 1..1000</a>
%H A005180 M. Aschbacher, <a href="http://www.ams.org/bull/1997-34-01/S0273-0979-97-00703-9/S0273-0979-97-00703-9.pdf">Review of "Classification of the finite simple groups, No. 2" by D. Gorenstein, R. Lyons & R. Solomon</a>
%H A005180 C. Cato, <a href="https://doi.org/10.1090/S0025-5718-1977-0430052-X">The orders of the known simple groups as far as one trillion</a>, Math. Comp., 31 (1977), 574-577.
%H A005180 Dept. of Pure Math., Univ. Sheffield, <a href="http://www.shef.ac.uk/~puremath/theorems/simple.html">The Classification of Finite Simple Groups</a>
%H A005180 D. Gorenstein, R. Lyons & R. Solomon, <a href="http://www.ams.org/online_bks/surv401">The Classification of the Finite Simple Groups</a>, AMS Books Online, Providence RI 1994.
%H A005180 D. Gorenstein, R. Lyons & R. Solomon, <a href="http://www.ams.org/online_bks/surv402">The Classification of the Finite Simple Groups, Number 2</a>, AMS Books Online, Providence RI 1996.
%H A005180 R. K. Guy and N. J. A. Sloane, <a href="/A005180/a005180.pdf">Correspondence</a>, 1988.
%H A005180 R. Solomon, <a href="https://doi.org/10.1090/S0273-0979-01-00909-0">A Brief History Of The Classification Of The Finite Simple Groups</a>, Bull. Amer. Math. Soc. 38 (2001), 315-352.
%H A005180 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%t A005180 (* Recomputation from A001034. *)
%t A005180 maxOrder = 7789;
%t A005180 A001034 = Select[Cases[Import["https://oeis.org/A001034/b001034.txt", "Table"], {_, _}][[All, 2]], # <= maxOrder&];
%t A005180 Union[{1}, Prime[Range[PrimePi[maxOrder]]], A001034] (* _Jean-François Alcover_, Aug 19 2019 *)
%Y A005180 Cf. A000001, A001228. Union of {1}, A000040 and A001034.
%K A005180 nonn,nice,easy
%O A005180 1,2
%A A005180 _N. J. A. Sloane_, _R. K. Guy_