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A231155
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Largest k such that no sum of digits is divisible by n (zeros not allowed in the digits of k).
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5
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9, 88, 999, 9999, 77777, 999999, 9999999, 88888888, 999999999, 9999999999, 77777777777, 999999999999, 9999999999999, 88888888888888, 999999999999999, 9999999999999999, 77777777777777777, 999999999999999999, 9999999999999999999
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OFFSET
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2,1
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COMMENTS
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a(n) has fewer than n digits, a special case of the fact that n integers always contain a sub(multi)set with a sum divisible by n.
The single digits appear to be periodic with period 210. - T. D. Noe, Nov 05 2013
This follows from the formula. Note also that the only digits which appear are 1, 5, 7, 8, and 9. - Charles R Greathouse IV, Nov 06 2013
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LINKS
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FORMULA
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a(n) consists of n-1 digits of d where d is the largest digit such that GCD(n,d)=1.
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EXAMPLE
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a(4) = 999 because none of 9, 9+9 or 9+9+9 are divisible by 4. All integers greater than 999 (with no zeros) have the property that some digit sum is divisible by 4, e.g., 1235 has 3+1.
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PROG
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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