

A048648


Order of nth stable homotopy group of spheres.


4



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

1,1


COMMENTS

Proved by Serre to be finite for all positive n.
The best current reference is IsaksenWangXu, Table 1.  Charles Rezk, Aug 22 2020


REFERENCES

D. B. Fuks, "Spheres, homotopy groups of the", Encyclopaedia of Mathematics, Vol. 8.
S. O. Kochman, Stable homotopy groups of spheres. A computerassisted approach. Lecture Notes in Mathematics, 1423. SpringerVerlag, Berlin, 1990. 330 pp. ISBN: 3540524681. [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.


LINKS

Charles Rezk, Table of n, a(n) for n = 1..81
A. Hatcher, Stable Homotopy Groups of Spheres
D. Isaksen, G. Wang, Z. Xu, More stable stems, arXiv:2001.04511 [math.AT], 2020.
S. O. Kochman and M. E. Mahowald, On the computation of stable stems, The Cech Centennial (Boston, MA, 1993), 299316, Contemp. Math., 181, Amer. Math. Soc., Providence, RI, 1995. [Math. Rev. 96j:55018]
John W. Milnor, Differential Topology Fortysix Years Later, Notices Amer. Math. Soc. 58 (2011), 804809.
Robert Scharein's program spherelink.c linked from the Linked Spheres page [has incorrect a(23) and a(29)a(33)]
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


AUTHOR

Stephen A. Silver


EXTENSIONS

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
More terms from Charles Rezk, Aug 25 2020


STATUS

approved



