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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 25 13:30 EST 2018. Contains 299654 sequences. (Running on oeis4.)