

A206242


In base n, for any integer k > 0, the least number a(n) such that the numbers k, 2k, ..., a(n)*k together include every basen digit.


2



2, 3, 6, 5, 20, 7, 28, 24, 72, 11, 99, 13, 104, 126, 120, 17, 272, 19, 304, 180, 336, 23, 414, 120, 400, 234, 432, 29, 783, 31, 496, 864, 1056, 850, 1120, 37, 1184, 1026, 1248, 41, 1476, 43, 1376, 1188, 1440, 47, 1692, 336, 1960, 1350, 1632, 53, 2544, 1350
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OFFSET

2,1


LINKS

David W. Wilson, Table of n, a(n) for n = 2..10000


FORMULA

a(n) = n if n prime; (n1)*A079277(n) otherwise.


EXAMPLE

In base 7, for any k > 0, the numbers k,2k,..,7k together included every base7 digit. k = 1 is the smallest number for which we need to go up to 7k to encounter digit 0 in 7k = 7 = 10(base 7). Hence A206242(7) = 7 and A206243(7) = 1.
In base 10, for any k > 0, the numbers k,2k,..,72k together include every base10 digit. k = 125 is the smallest number for which we need to go up to 72k = 9000 to encounter digit 9. Hence A206242(10) = 72 and A206243(7) = 125.


CROSSREFS

Cf. A206243 (smallest value of k for which a(n) is required).
Sequence in context: A156833 A319344 A260443 * A124655 A066838 A228151
Adjacent sequences: A206239 A206240 A206241 * A206243 A206244 A206245


KEYWORD

nonn,base


AUTHOR

David W. Wilson, Feb 05 2012


STATUS

approved



