A206242 a(n) is the least number j such that, for any integer k > 0, the base-n representations of the numbers k, 2k, ..., j*k together include every base-n digit.

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

Offset: 2

Author

David W. Wilson, Feb 05 2012

Keywords

• nonn
• base

Examples

			In base 7, for any k > 0, the numbers k,2k,...,7k together include every base-7 digit. k = 1 is the smallest number for which we need to go up to 7k to encounter digit 0 in 7k = 7 = 10_7. Hence a(7) = 7 and A206243(7) = 1.
In base 10, for any k > 0, the numbers k,2k,...,72k together include every base-10 digit. k = 125 is the smallest number for which we need to go up to 72k = 9000 to encounter digit 9. Hence a(10) = 72 and A206243(7) = 125.
		

Links

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

Crossrefs

Cf. A079277, A206243 (smallest value of k for which a(n) is required).

Formula

a(n) = n if n prime; (n-1)*A079277(n) otherwise.