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 A208576 #19 Apr 06 2020 20:06:16 %S A208576 0,0,1,1,1,2,1,1,1,1,1,2,1,1,1,2,1,2,1,1,1,2,1,2,1,1,1,1,1,1,1,1,1,1, %T A208576 1,2,1,1,1,2,1,2,1,1,1,2,1,2,1,1,1,1,1,1,1,1,1,2,1,2,1,1,1,2,1,2,1,1, %U A208576 1,2,1,2,1,1,1,1,1,1,1,1,1,2,1,2,1,1,1,2,1,2 %N A208576 Multiplicative persistence of n in factorial base. %C A208576 Diamond and Reidpath prove that a(2n) = 1 for n > 0, a(n) = 2 if n is contains an even digit but no 0's in its factorial base representation. If a(n) > 2 then 3 | n. %C A208576 Further modular properties can be easily proved. For example, a(n) > 2 implies that n is 33, 45, 81, or 93 mod 120. %H A208576 Antti Karttunen, <a href="/A208576/b208576.txt">Table of n, a(n) for n = 0..65537</a> %H A208576 M. R. Diamond and D. D. Reidpath, <a href="http://www.mathe2.uni-bayreuth.de/sascha/oeis/persistence/PERSIST.PDF">A counterexample to conjectures by Sloane and Erdos concerning the persistence of numbers</a>, Journal of Recreational Mathematics 29:2 (1998), pp. 89-92. %H A208576 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a> %F A208576 a(0) = a(1) = 0; for n > 1, a(n) = 1 + a(A208575(n)). - _Antti Karttunen_, Nov 14 2018 %o A208576 (PARI) pr(n)=my(k=1,s=1);while(n,s*=n%k++;n\=k);s %o A208576 a(n)=my(t);while(n>1,t++;n=pr(n));t %Y A208576 Cf. A007623, A031346, A208575, A208277. %K A208576 nonn,base %O A208576 0,6 %A A208576 _Charles R Greathouse IV_, Feb 28 2012