1,3

Suppose n has d digits; then the sum of its digits is <= 729d and n >= 10^(d-1). So d <= 5. It is now easy to check that the numbers shown are the only solutions.

A055012(a(n))=a(n); A165331(a(n))=0; subset of A165332. [From Reinhard Zumkeller, Sep 17 2009]

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 153, p. 50, Ellipses, Paris 2008.

G. H. Hardy, A Mathematician's Apology, Cambridge, 1967.

H. Lehning, "La migration des nombres vers le bonheur" in 'Tangente:L'aventure mathematique' pp. 27 No. 108 Jan-Feb 2006 Pole Paris.

J. Shallit, Number theory and formal languages, in Emerging applications of number theory (Minneapolis, MN, 1996), 547-570, IMA Vol. Math. Appl., 109, Springer, New York, 1999.

Table of n, a(n) for n=1..6.

Cf. A005188, A023052, A046156.

A165330, A035504, A008585, A165333, A165334, A165335. [From Reinhard Zumkeller, Sep 17 2009]

Cf. A052455, A052464, A124068, A124069, A226970, A003321.

Sequence in context: A194660 A159294 A066528 * A056733 A199851 A181775

Adjacent sequences:  A046194 A046195 A046196 * A046198 A046199 A046200

nonn,fini,full,base

Richard Schroeppel

approved