

A046197


Fixed points for operation of repeatedly replacing a number with the sum of the cubes of its digits.


26




OFFSET

1,3


COMMENTS

Suppose n has d digits; then the sum of the cubes of its digits is <= 729d and n >= 10^(d1). So d <= 5. It is now easy to check that the numbers shown are the only solutions. [Corrected by M. F. Hasler, Apr 12 2015]
This is row n=3 of A252648.  M. F. Hasler, Apr 12 2015


REFERENCES

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.
J. Shallit, Number theory and formal languages, in Emerging applications of number theory (Minneapolis, MN, 1996), 547570, IMA Vol. Math. Appl., 109, Springer, New York, 1999.


LINKS

Table of n, a(n) for n=1..6.
H. Lehning, La migration des nombres vers le bonheur, Tangente: L'aventure mathématique, pp. 27 No. 108 JanFeb 2006 Pole Paris.


FORMULA

A055012(a(n))=a(n); A165331(a(n))=0; subset of A031179.  Reinhard Zumkeller, Sep 17 2009


EXAMPLE

1^3 + 5^3 + 3^3 = 153. 3^3+7^3 +0^3 = 370.


PROG

(PARI) for(n=0, 10^5, A055012(n)==n&&print1(n", ")) \\ M. F. Hasler, Apr 12 2015


CROSSREFS

Cf. A005188, A023052, A046156.
Cf. A165330, A035504, A008585, A165333, A165334, A165335.
Cf. A052455, A052464, A124068, A124069, A226970, A003321.
Sequence in context: A332228 A349755 A066528 * A271730 A056733 A256748
Adjacent sequences: A046194 A046195 A046196 * A046198 A046199 A046200


KEYWORD

nonn,fini,full,base


AUTHOR

Richard C. Schroeppel


STATUS

approved



