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%I #38 Dec 09 2014 03:35:43
%S 9,88,999,9999,77777,999999,9999999,88888888,999999999,9999999999,
%T 77777777777,999999999999,9999999999999,88888888888888,
%U 999999999999999,9999999999999999,77777777777777777,999999999999999999,9999999999999999999
%N Largest k such that no sum of digits is divisible by n (zeros not allowed in the digits of k).
%C 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.
%C The single digits appear to be periodic with period 210. - _T. D. Noe_, Nov 05 2013
%C 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
%F a(n) consists of n-1 digits of d where d is the largest digit such that GCD(n,d)=1.
%F a(n) = A231470(n)*(10^(n-1)-1)/9. - _M. F. Hasler_, Nov 09 2013
%e 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.
%o (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
%Y Subsequence of A010785.
%K nonn,base,easy
%O 2,1
%A _Jon Perry_, Nov 04 2013
%E a(9)-a(20) from _Charles R Greathouse IV_, Nov 05 2013
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