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A206242
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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.
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2
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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
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2,1
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LINKS
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FORMULA
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a(n) = n if n prime; (n-1)*A079277(n) otherwise.
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EXAMPLE
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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.
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CROSSREFS
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Cf. A079277, A206243 (smallest value of k for which a(n) is required).
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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