%I
%S 10,45,10,23,18,15,10,12,10,9,10,13,8,17,12,16,7,5,10,45,9,9,9,19,36,
%T 15,7,17,7,9,10,18,10,27,16,11,10,5,10,23,9,9,7,9,8,11,10,12,10,18,9,
%U 18,8,11,9,12,10,5,10,15,9,9,8
%N The first a(n) positive multiples of n together include every digit.
%C The maximum value of this sequence is a(n) = 72, first attained with n = 125. This can be proved via analysis mod 10^4 (T. Rockicki). a(n) = 72 for an infinite number of n including n = 125*10^k.
%H David W. Wilson, <a href="/A202296/b202296.txt">Table of n, a(n) for n = 1..10000</a>
%e The first 7 multiples of 17 (17,34,51,68,85,102,119) together include every digit, so a(17) = 7.
%t multInclD[n_, b_:10] := Module[{curr = 1, notFound = True}, While[notFound, If[Union[Flatten[Table[IntegerDigits[n * k, b], {k, curr}]]] == Range[0, b  1], notFound = False, curr++]]; Return[curr]]; Table[multInclD[n], {n, 70}] (* _Alonso del Arte_, Dec 15 2011 *)
%K nonn,base
%O 1,1
%A _David W. Wilson_, Dec 15 2011
