

A277059


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


3



1, 4, 6, 14, 45, 370, 588, 3364, 11115, 168496, 271458, 2442138
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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^m1)/(n1) + m  1;
for n=4m+1, a(n) = (n^(2m)1)(n^2+1) / (2(n^21)) + m;
for n=4m1, a(n) = (n^(2m2)1)(n^2+1) / (2(n^21)) + m + n^(2m1).


EXAMPLE

Any binary repunit itself contains a 1, so a(2)=1.
kth 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



