A231155 Largest k such that no sum of digits is divisible by n (zeros not allowed in the digits of k).

9, 88, 999, 9999, 77777, 999999, 9999999, 88888888, 999999999, 9999999999, 77777777777, 999999999999, 9999999999999, 88888888888888, 999999999999999, 9999999999999999, 77777777777777777, 999999999999999999, 9999999999999999999

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 * A376145 A279166 A147884

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