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

Author

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

Keywords

• base
• more
• nonn

Comments

Length of the largest polydivisible number in base n.

Examples

			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.
		

Links

• A. Mihailovs, Ponder This.
• Wikipedia, Polydivisible number.

Crossrefs

Cf. A109032.

Programs

Maple

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

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

Extensions

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