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 A208277 #21 Jan 21 2013 01:35:07 %S A208277 0,2,5,633,443153013 %N A208277 Smallest number of multiplicative persistence n in factorial base. %C A208277 a(n) exists for all n, unlike (conjecturally) its decimal equivalent A003001. In particular, with k = a(n-1), a(n) <= k * k! + (k-1)! + ... + 2! + 1! < (a(n-1)+1)! for n > 1. Diamond & Reidpath ask if this upper bound can be improved. %C A208277 a(5) <= 255429978433810461138446192454297813. %H A208277 M. R. Diamond and D. D. Reidpath, <a href="http://www.markdiamond.com.au/download/multiplicative-persistence-of-a-numbers.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. %e A208277 5 = 1*1!+2*2!, and so is 21 in factorial base; the product of its digits is 2*1 = 10_! and the product of its digits in factorial base is 0*1 = 0, so 5 has multiplicative persistence 2. Since it is the smallest, a(2) = 5. %e A208277 633 = 51111_! -> 21_! -> 10_! -> 0_! is the least chain of length 3 and so a(3) = 633. %o A208277 (PARI) pr(n)=my(k=1,s=1);while(n,s*=n%k++;n\=k);s %o A208277 persist(n)=my(t); while(n>1, t++; n=pr(n)); t %o A208277 a(n)=my(k=0);while(persist(k)!=n, k++); k \\ _Charles R Greathouse IV_, Jan 21 2013 %Y A208277 Cf. A003001, A007623, A031346, A208575, A208576. %K A208277 nonn,base,more %O A208277 0,2 %A A208277 _Charles R Greathouse IV_, Feb 28 2012