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A046197 Fixed points for operation of repeatedly replacing a number with the sum of the cubes of its digits. 26
0, 1, 153, 370, 371, 407 (list; graph; refs; listen; history; text; internal format)



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


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), 547-570, IMA Vol. Math. Appl., 109, Springer, New York, 1999.


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 Jan-Feb 2006 Pole Paris.


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


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


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


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




Richard C. Schroeppel



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Last modified November 26 03:33 EST 2022. Contains 358353 sequences. (Running on oeis4.)