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A231155 Largest k such that no sum of digits is divisible by n (zeros not allowed in the digits of k). 5
9, 88, 999, 9999, 77777, 999999, 9999999, 88888888, 999999999, 9999999999, 77777777777, 999999999999, 9999999999999, 88888888888888, 999999999999999, 9999999999999999, 77777777777777777, 999999999999999999, 9999999999999999999 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

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

LINKS

Table of n, a(n) for n=2..20.

FORMULA

a(n) consists of n-1 digits of d where d is the largest digit such that GCD(n,d)=1.

a(n) = A231470(n)*(10^(n-1)-1)/9. - M. F. Hasler, Nov 09 2013

EXAMPLE

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.

PROG

(PARI) a(n)=forstep(k=9, 1, -1, if(gcd(n, k)==1, return(10^(n-1)\9*k))) \\ Charles R Greathouse IV, Nov 05 2013

CROSSREFS

Subsequence of A010785.

Sequence in context: A260041 A084022 A084015 * A279166 A147884 A178369

Adjacent sequences:  A231152 A231153 A231154 * A231156 A231157 A231158

KEYWORD

nonn,base,easy

AUTHOR

Jon Perry, Nov 04 2013

EXTENSIONS

a(9)-a(20) from Charles R Greathouse IV, Nov 05 2013

STATUS

approved

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Last modified October 22 04:29 EDT 2018. Contains 316431 sequences. (Running on oeis4.)