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A353087 Smallest integer k such that k! contains at least n copies of each decimal digit.

%I A353087 #18 Apr 23 2022 01:40:53
%S A353087 23,34,40,55,59,67,75,81,90,90,97,108,118,123,131,144,147,147,147,157,
%T A353087 157,182,186,186,186,189,203,204,206,206,209,232,232,236,236,237,237,
%U A353087 245,257,257,265,278,282,282,282,282,282,290,307,307,318,318,318,318,341
%N A353087 Smallest integer k such that k! contains at least n copies of each decimal digit.
%H A353087 Alois P. Heinz, <a href="/A353087/b353087.txt">Table of n, a(n) for n = 1..5000</a>
%e A353087 23! = 25852016738884976640000 is the smallest factorial containing at least one copy of each decimal digit. Thus a(1) = 23.
%p A353087 a:= proc(n) option remember; local k; for k from a(n-1)
%p A353087       while min((p-> seq(coeff(p, x, j), j=0..9))(add(
%p A353087             x^i, i=convert(k!, base, 10))))<n do od; k
%p A353087     end: a(0):=0:
%p A353087 seq(a(n), n=1..100);
%o A353087 (Python)
%o A353087 def A353087(n):
%o A353087     k, m, r  = 1, 1, 10**(10*n-1)
%o A353087     while m < r:
%o A353087         k += 1
%o A353087         m *= k
%o A353087     s = str(m)
%o A353087     while any(s.count(d) < n for d in '0123456789'):
%o A353087         k += 1
%o A353087         m *= k
%o A353087         s = str(m)
%o A353087     return k # _Chai Wah Wu_, Apr 22 2022
%Y A353087 Cf. A000142, A352040.
%K A353087 nonn,base
%O A353087 1,1
%A A353087 _Alois P. Heinz_, Apr 22 2022