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A046197 Fixed points for operation of repeatedly replacing a number with the sum of the cubes of its digits. 24
0, 1, 153, 370, 371, 407 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Suppose n has d digits; then the sum of the cubes 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. [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.

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.

LINKS

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

FORMULA

A055012(a(n))=a(n); A165331(a(n))=0; subset of A165332. - 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: A194660 A159294 A066528 * A271730 A056733 A256748

Adjacent sequences:  A046194 A046195 A046196 * A046198 A046199 A046200

KEYWORD

nonn,fini,full,base

AUTHOR

Richard C. Schroeppel

STATUS

approved

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Last modified November 17 08:39 EST 2019. Contains 329217 sequences. (Running on oeis4.)