

A109783


a(n) is the largest possible K such that there exists a Kdigit 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.


3



2, 6, 7, 10, 11, 18, 17, 22, 25, 26, 28, 35, 39, 38, 39, 45, 48, 48, 52, 53, 56, 58, 61, 65, 67, 69, 73, 75, 79, 83, 83
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

2,1


COMMENTS

Length of the largest polydivisible number in base n.


LINKS

Table of n, a(n) for n=2..32.
A. Mihailovs, Ponder This.
Wikipedia, Polydivisible number.


FORMULA

Conjecture 1: a(n) is finite for all n>1. Conjecture 2: a(n) ~ n*e.
a(n) = 1 + floor( log(A109032(n)) / log(n) ).  Max Alekseyev, Sep 19 2009


EXAMPLE

a(10)=25 because for 25digit 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 26digit number with similar properties.


MAPLE

a:=seq(nops(convert(A109032[i], base, i+1)), i=1..nops(A109032)); # Martin Renner, Apr 05 2016


CROSSREFS

Cf. A109032.
Sequence in context: A341437 A327985 A189465 * A186888 A179883 A179303
Adjacent sequences: A109780 A109781 A109782 * A109784 A109785 A109786


KEYWORD

base,more,nonn


AUTHOR

Alec Mihailovs (alec(AT)mihailovs.com), Aug 13 2005


EXTENSIONS

a(24)a(32) from Karl W. Heuer, Jan 08 2015


STATUS

approved



