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%I #15 Apr 14 2023 19:59:20
%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 18,8,11,9,12,10,5,10,15,9,9,8,9,11,11,7,14,5,8,10,11
%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 (_Tomas Rokicki_). 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 *)
%o (Python)
%o def a(n):
%o s = set()
%o return next(i for i in range(1, 73) if len(s:=s|set(str(i*n)))==10)
%o print([a(n) for n in range(1, 73)]) # _Michael S. Branicky_, Apr 14 2023
%K nonn,base
%O 1,1
%A _David W. Wilson_, Dec 15 2011
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