

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
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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 n1 digits of d where d is the largest digit such that GCD(n,d)=1.
a(n) = A231470(n)*(10^(n1)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^(n1)\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



