This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A046197 #43 May 25 2025 09:25:00 %S A046197 0,1,153,370,371,407 %N A046197 Fixed points for operation of repeatedly replacing a number with the sum of the cubes of its digits. %C A046197 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] %C A046197 This is row n=3 of A252648. - _M. F. Hasler_, Apr 12 2015 %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 Alfred S. Posamentier, Math Charmers, Tantalizing Tidbits for the Mind, Prometheus Books, NY, 2003, pages 60-62. %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. %D A046197 David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 140. %H A046197 H. Lehning, <a href="https://www.lehning.eu/uploads/1/2/0/8/120804163/articletangente_108_janvier_2006_la_migration_des_nombres_vers_le_bonheur.pdf">La migration des nombres vers le bonheur</a>, Tangente: L'aventure mathématique, pp. 27 No. 108 Jan-Feb 2006 Pole Paris. %F A046197 A055012(a(n))=a(n); A165331(a(n))=0; subset of A031179. - _Reinhard Zumkeller_, Sep 17 2009 %e A046197 1^3 + 5^3 + 3^3 = 153. 3^3+7^3 +0^3 = 370. %t A046197 Select[Range[0,407],Total[IntegerDigits[#]^3]==# &] (* _Stefano Spezia_, Sep 08 2024 *) %o A046197 (PARI) for(n=0,10^5,A055012(n)==n&&print1(n",")) \\ _M. F. Hasler_, Apr 12 2015 %Y A046197 Cf. A005188, A023052, A046156. %Y A046197 Cf. A165330, A035504, A008585, A165333, A165334, A165335. %Y A046197 Cf. A052455, A052464, A124068, A124069, A226970, A003321. %K A046197 nonn,fini,full,base %O A046197 1,3 %A A046197 Richard C. Schroeppel