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A048648
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Order of n-th stable homotopy group of spheres.
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5
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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, 12, 24, 2, 3, 6, 65280, 16, 32, 32, 114912, 6, 12, 120, 1267200, 384, 32, 96, 552, 8, 5760, 48, 12579840, 64, 12, 24, 384, 24, 16, 8, 20880, 2, 8, 4, 687456, 4, 1
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OFFSET
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1,1
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COMMENTS
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Proved by Serre to be finite for all positive n.
The best current reference is Isaksen-Wang-Xu, Table 1. - Charles Rezk, Aug 22 2020
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REFERENCES
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D. B. Fuks, "Spheres, homotopy groups of the", Encyclopaedia of Mathematics, Vol. 8.
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]
Douglas C. Ravenel, Complex cobordism and stable homotopy groups of spheres, AMS Chelsea Publishing, 2003.
Hirosi Toda, Composition Methods in Homotopy Groups of Spheres, Princeton University Press, 1962.
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LINKS
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S. O. Kochman and M. E. Mahowald, On the computation of stable stems, The Cech Centennial (Boston, MA, 1993), 299-316, Contemp. Math., 181, Amer. Math. Soc., Providence, RI, 1995. [Math. Rev. 96j:55018]
Robert Scharein's program sphere-link.c linked from the Linked Spheres page [has incorrect a(23) and a(29)-a(33)]
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FORMULA
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a(n) = |Pi_n^S| = |Pi_{k+n}(S^k)| for k > n+1.
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EXAMPLE
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Pi_1^S = Pi_4(S^3) = Z/2Z, so a(1) = |Z/2Z| = 2.
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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More terms from Alex Fink (finka(AT)math.ucalgary.ca), Aug 10 2006
a(23) and a(29)-a(33) corrected by Charles Rezk, Aug 22 2020
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STATUS
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approved
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