1,7

For n not equal to 4 (and possibly for all n) this is the number of oriented diffeomorphism classes of differentiable structures on the n-sphere.

a(3) = 1 follows now that the Poincare conjecture has been proved.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

M. A. Kervaire and J. W. Milnor, Groups of homotopy spheres: I. Ann. of Math. (2) 77 1963 504-537.

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]

J. P. Levine, Lectures on groups of homotopy spheres. In Algebraic and geometric topology (New Brunswick, NJ, 1983), 62-95, Lecture Notes in Math., 1126, Springer, Berlin, 1985.

J. W. Milnor, On manifolds homeomorphic to the 7-sphere, Ann. of Math. 64 (1956), 399-405.

J. W. Milnor and J. D. Stasheff, Characteristic Classes, Princeton, 1974, p. 285.

S. P. Novikov ed., Topology I, Encyc. of Math. Sci., vol. 12.

H. Whitney, The work of John W. Milnor, pp. 48-50 of Proc. Internat. Congress Mathematicians, Stockholm, 1962.

A. Hatcher, Stable Homotopy Groups of Spheres

N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Cf. A047680, A053381, A057617, A048648.

Sequence in context: A040780 A013550 A040781 this_sequence A040782 A040783 A057617

Adjacent sequences: A001673 A001674 A001675 this_sequence A001677 A001678 A001679

nonn,hard,nice

N. J. A. Sloane (njas(AT)research.att.com).