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A048648 Order of n-th stable homotopy group of spheres. 3
2, 2, 24, 1, 1, 2, 240, 4, 8, 6, 504, 1, 3, 4, 960, 4, 16, 16, 528, 24, 4, 4, 1048320, 4, 4, 12, 24, 2, 1, 2, 32640, 4, 64 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Proved by Serre to be finite for all positive n.

REFERENCES

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]

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]

Douglas C. Ravenel, Complex cobordism and stable homotopy groups of spheres, AMS Chelsea Publishing, 2003.

Robert Scharein's program sphere-link.c linked from www.pims.math.ca/knotplot/links/sphere.html

Hirosi Toda, Composition Methods in Homotopy Groups of Spheres, Princeton University Press, 1962.

LINKS

Table of n, a(n) for n=1..33.

A. Hatcher, Stable Homotopy Groups of Spheres

John W. Milnor, Differential Topology Forty-six Years Later, Notices Amer. Math. Soc. 58 (2011), 804-809.

Wikipedia, Homotopy groups of spheres

FORMULA

a(n) = |Pi_n^S| = |Pi_{k+n}(S^k)| for k > n+1.

EXAMPLE

Pi_1^S = Pi_4(S^3) = Z/2Z, so a(1) = |Z/2Z| = 2.

CROSSREFS

Cf. A001676.

Sequence in context: A014358 A093355 A122962 * A229334 A120065 A250033

Adjacent sequences:  A048645 A048646 A048647 * A048649 A048650 A048651

KEYWORD

nonn,nice,more

AUTHOR

Stephen A. Silver

EXTENSIONS

More terms from Alex Fink (finka(AT)math.ucalgary.ca), Aug 10 2006

STATUS

approved

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Last modified July 23 14:59 EDT 2017. Contains 289688 sequences.