%I A046197
%S A046197 0,1,153,370,371,407
%N A046197 Fixed points for operation of repeatedly replacing a number by the sum 
               of the cubes of its digits.
%C A046197 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.
%C A046197 A055012(a(n))=a(n); A165331(a(n))=0; subset of A165332. [From Reinhard 
               Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 17 2009]
%D A046197 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 153, p. 50, Ellipses, 
               Paris 2008.
%D A046197 G. H. Hardy, A Mathematician's Apology, Cambridge, 1967.
%D A046197 H. Lehning, "La migration des nombres vers le bonheur" in 'Tangente:L'aventure 
               mathematique' pp. 27 No. 108 Jan-Feb 2006 Pole Paris.
%D A046197 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.
%Y A046197 Cf. A005188, A023052, A046156.
%Y A046197 A165330, A035504, A008585, A165333, A165334, A165335. [From Reinhard 
               Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 17 2009]
%Y A046197 Sequence in context: A104810 A159294 A066528 this_sequence A056733 A050209 
               A109142
%Y A046197 Adjacent sequences: A046194 A046195 A046196 this_sequence A046198 A046199 
               A046200
%K A046197 nonn,fini,full,base
%O A046197 1,3
%A A046197 Richard Schroeppel (rschroe(AT)sandia.gov)