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

Author

Jon Perry, Nov 04 2013

Keywords

• nonn
• base
• easy

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

Examples

			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.
		

Crossrefs

Subsequence of A010785.

Programs

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

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

Extensions

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