%I A109783
%S A109783 2,6,7,10,11,18,17,22,25,26,28,35,39,38,39,45,48,48,52,53,56,58
%N A109783 a(n) is the largest possible K such that there exists a K-digit in base 
               n integer M such that for each N=1,2,...,K, the integer given by 
               the first N digits of M in base n is divisible by N.
%H A109783 A. Mihailovs, <a href="http://beta.mapleprimes.com/blog/alec/ponder_this">
               Ponder This</a>.
%F A109783 Conjecture 1. a(n) is finite for all n>1. Conjecture 2. a(n) ~ n*e.
%F A109783 a(n) = 1 + floor( log(A109032(n)) / log(n) ) [From Max Alekseyev (maxale(AT)gmail.com), 
               Sep 19 2009]
%e A109783 a(10)=25 because for 25-digit number 3608528850368400786036725, 3 is 
               divisible by 1, 36 is divisible by 2, 360 is divisible by 3, ..., 
               3608528850368400786036725 is divisible by 25 and there is no 26-digit 
               number with similar properties.
%Y A109783 Cf. A109032.
%Y A109783 Sequence in context: A020897 A020898 A047277 this_sequence A030309 A074223 
               A029459
%Y A109783 Adjacent sequences: A109780 A109781 A109782 this_sequence A109784 A109785 
               A109786
%K A109783 base,more,nonn
%O A109783 2,1
%A A109783 Alec Mihailovs (alec(AT)mihailovs.com), Aug 13 2005