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.

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

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: 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