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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.

%I A109783 #21 Aug 30 2021 10:51:46
%S A109783 2,6,7,10,11,18,17,22,25,26,28,35,39,38,39,45,48,48,52,53,56,58,61,65,
%T A109783 67,69,73,75,79,83,83
%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.
%C A109783 Length of the largest polydivisible number in base n.
%H A109783 A. Mihailovs, <a href="http://beta.mapleprimes.com/blog/alec/ponder_this">Ponder This</a>.
%H A109783 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polydivisible_number">Polydivisible number</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) ). - _Max Alekseyev_, 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.
%p A109783 a:=seq(nops(convert(A109032[i],base,i+1)),i=1..nops(A109032)); # _Martin Renner_, Apr 05 2016
%Y A109783 Cf. A109032.
%K A109783 base,more,nonn
%O A109783 2,1
%A A109783 Alec Mihailovs (alec(AT)mihailovs.com), Aug 13 2005
%E A109783 a(24)-a(32) from _Karl W. Heuer_, Jan 08 2015