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%I #31 Dec 21 2024 11:08:36
%S 2,4,6,8,10,12,14,16,18,0,22,36,26,28,30,32,34,36,38,0,63,44,46,96,
%T 100,78,54,56,58,0,62,64,66,68,70,72,111,76,78,0,82,168,86,88,90,92,
%U 188,96,588,0,204
%N Smallest multiple of n which uses no digits of n, or 0 if no such number exists.
%C For numbers n of the form 10k, of the form 10k+5 with a zero somewhere, and those using all 10 digits, a(n) = 0.
%C Are there numbers using 8 of the 9 nonzero digits for which a(n) is nonzero? If so, what is the smallest such number?
%C All such numbers have a(n) nonzero since a candidate value for a(n) is d*A052983(n) where d is the nonzero digit not in n. - _Gonzalo Martínez_, Dec 12 2024
%H Michel Marcus, <a href="/A074157/b074157.txt">Table of n, a(n) for n = 1..1000</a>
%o (PARI) a(n) = {if (! (n % 10), return (0)); my(dn = Set(digits(n)), m = 2*n); if (#dn == 10, return (0)); if (!(n % 5) && vecsearch(dn, 0), return (0)); while(#setintersect(Set(digits(m)), dn), m += n); m;} \\ _Michel Marcus_, Aug 04 2017
%Y Cf. A052983.
%K base,nonn
%O 1,1
%A _Amarnath Murthy_, Aug 29 2002
%E a(24) and a(49) corrected by _Michel Marcus_, Aug 04 2017