A277059 Least k such that any sufficiently long repunit multiplied by k contains all nonzero digits in base n.

1, 4, 6, 14, 45, 370, 588, 3364, 11115, 168496, 271458, 2442138

Offset: 2

Author

Andrey Zabolotskiy and Altug Alkan, Sep 26 2016

Keywords

• nonn
• base
• more

Comments

Trailing terms of rows of A277058.

Written in base n, the terms read: 1, 11, 12, 24, 113, 1036, 1114, 4547, 11115, 105659, 111116, 67676A, ...

Examples

			Any binary repunit itself contains a 1, so a(2)=1.
k-th decimal repunit for k>4 multiplied by 11115 contains all nonzero decimal digits (see A277057) with no number less than 11115 having the same property, so a(10)=11115.
		

Crossrefs

Cf. A002275, A277056, A277057, A277058.

Formula

Conjecture:

for n=2m, a(n) = (n^m-1)/(n-1) + m - 1;

for n=4m+1, a(n) = (n^(2m)-1)(n^2+1) / (2(n^2-1)) + m;

for n=4m-1, a(n) = (n^(2m-2)-1)(n^2+1) / (2(n^2-1)) + m + n^(2m-1).