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

2,2

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, ...

Links

Table of n, a(n) for n=2..13.

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).

Example

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.

Sequence in context: A219774 A274208 A077068 * A096003 A114058 A214901

Adjacent sequences: A277056 A277057 A277058 * A277060 A277061 A277062

Keyword

nonn,base,more

Author

Andrey Zabolotskiy and Altug Alkan, Sep 26 2016

Status

approved