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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. 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 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.

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: A200926 A047277 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

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Last modified March 26 22:42 EDT 2019. Contains 321565 sequences. (Running on oeis4.)