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 A193585 #25 Jan 05 2025 19:51:39 %S A193585 0,1,0,1,1,2,3,2,1,2,4,3,2,7,1,2,1,3,1,6,2,8,4,6,1,5,4,6,2,8,6,5,3,5, %T A193585 4,5,3,6,1,7,6,6,2,5,4,11,4,4,4,6,3,11,4,9,4,8,4,6,6,5,4,9,6,5,2,6,3, %U A193585 7,7,8,5,14,5,8,3,6,3,4,5,10,5,10,6,8,5 %N A193585 Number of cycles under iteration of sum of squares of digits in base b. %C A193585 If b>=2 and a>=b^2 then S(a,2,b)<a. For each positive integer a, there is an positive integer m such that S^m(a,2,b)<b^2. (Grundman/Teeple, 2001, Lemma 6 and Corollary 7). %H A193585 Martin Renner, <a href="/A193585/b193585.txt">Table of n, a(n) for n = 2..300</a> %H A193585 H. G. Grundman, E. A. Teeple, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/39-5/grundman.pdf">Generalized Happy Numbers</a>, Fibonacci Quarterly 39 (2001), nr. 5, p. 462-466. %e A193585 In the decimal system all integers go to (1) or (4, 16, 37, 58, 89, 145, 42, 20) under the iteration of sum of squares of digits, hence there is one fixed point and one cycle. Therefore a(10) = 1. %Y A193585 Cf. A193583, A193586. %K A193585 nonn,base %O A193585 2,6 %A A193585 _Martin Renner_, Jul 31 2011