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%I #45 Sep 14 2023 00:48:21
%S 2,2,24,1,1,2,240,4,8,6,504,1,3,4,960,4,16,16,528,24,4,4,3144960,4,4,
%T 12,24,2,3,6,65280,16,32,32,114912,6,12,120,1267200,384,32,96,552,8,
%U 5760,48,12579840,64,12,24,384,24,16,8,20880,2,8,4,687456,4,1
%N Order of n-th stable homotopy group of spheres.
%C Proved by Serre to be finite for all positive n.
%C The best current reference is Isaksen-Wang-Xu, Table 1. - _Charles Rezk_, Aug 22 2020
%D D. B. Fuks, "Spheres, homotopy groups of the", Encyclopaedia of Mathematics, Vol. 8.
%D S. O. Kochman, Stable homotopy groups of spheres. A computer-assisted approach. Lecture Notes in Mathematics, 1423. Springer-Verlag, Berlin, 1990. 330 pp. ISBN: 3-540-52468-1. [Math. Rev. 91j:55016]
%D Douglas C. Ravenel, Complex cobordism and stable homotopy groups of spheres, AMS Chelsea Publishing, 2003.
%D Hirosi Toda, Composition Methods in Homotopy Groups of Spheres, Princeton University Press, 1962.
%H Andrey Zabolotskiy, <a href="/A048648/b048648.txt">Table of n, a(n) for n = 1..83</a> (terms 1..81 from Charles Rezk, terms 82..83 using data from Isaksen, Wang & Xu (2023))
%H Kevin Hartnett, <a href="https://www.quantamagazine.org/an-old-conjecture-falls-making-spheres-a-lot-more-complicated-20230822/">An Old Conjecture Falls, Making Spheres a Lot More Complicated</a>, Quanta Magazine (2023)
%H A. Hatcher, <a href="http://www.math.cornell.edu/~hatcher/stemfigs/stems.html">Stable Homotopy Groups of Spheres</a>
%H Daniel C. Isaksen, Guozhen Wang and Zhouli Xu, <a href="https://doi.org/10.1007/s10240-023-00139-1">Stable homotopy groups of spheres: from dimension 0 to 90</a>, Publications mathématiques de l'IHÉS, 137 (2023), 107-243; arXiv:<a href="https://arxiv.org/abs/2001.04511">2001.04511</a> [math.AT], 2020-2023.
%H S. O. Kochman and M. E. Mahowald, <a href="https://www.uio.no/studier/emner/matnat/math/MAT9580/v15/undervisningsmateriale/kochman-mahowald-conm181-1995.pdf">On the computation of stable stems</a>, The Cech Centennial (Boston, MA, 1993), 299-316, Contemp. Math., 181, Amer. Math. Soc., Providence, RI, 1995. [Math. Rev. 96j:55018]
%H John W. Milnor, <a href="http://www.ams.org/notices/201106/rtx110600804p.pdf">Differential Topology Forty-six Years Later</a>, Notices Amer. Math. Soc. 58 (2011), 804-809.
%H Robert Scharein's program sphere-link.c linked from the <a href="https://knotplot.com/links/sphere.html">Linked Spheres</a> page [has incorrect a(23) and a(29)-a(33)]
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Homotopy_groups_of_spheres">Homotopy groups of spheres</a>
%F a(n) = |Pi_n^S| = |Pi_{k+n}(S^k)| for k > n+1.
%e Pi_1^S = Pi_4(S^3) = Z/2Z, so a(1) = |Z/2Z| = 2.
%Y Cf. A001676.
%K nonn,nice
%O 1,1
%A _Stephen A. Silver_
%E More terms from Alex Fink (finka(AT)math.ucalgary.ca), Aug 10 2006
%E a(23) and a(29)-a(33) corrected by _Charles Rezk_, Aug 22 2020
%E More terms from _Charles Rezk_, Aug 25 2020
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