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%I #20 Jun 01 2024 14:30:10
%S 2,2,5,5,3,2,2,5,5,3,2,2,3,5,4,6,5,5,5,7,5,3,4,7,3,2,8,2,5,3,5,4,3,3,
%T 3,6,6,5,4,3,3,6,7,4,3,4,4,4,4,3,2,3,7,5,3,2,3,5,5,3,2,3,5,2,2,3,2,3,
%U 4,5,5,3,3,3,2,3,2,5,5,5,5
%N a(n) = minimum k>1 such that n^k contains all distinct decimal digits of n.
%H Michel Marcus, <a href="/A373203/b373203.txt">Table of n, a(n) for n = 0..10000</a>
%F A253600(n) <= a(n) <= A045537(n). - _Michael S. Branicky_, May 28 2024
%F A111442(n) = n^a(n).
%e For n=12, a(12)=3 because 12^3=1728 contains all decimal digits of n. Compare to A253600(12)=2 because 12^2=144 contains any digit of n.
%t seq={}; Do[k=1;Until[ContainsAll[IntegerDigits[n^k],IntegerDigits[n] ],k++];AppendTo[seq,k] ,{n,0,80}];seq
%o (Python)
%o from itertools import count
%o def a(n):
%o s = set(str(n))
%o return next(k for k in count(2) if s <= set(str(n**k)))
%o print([a(n) for n in range(81)]) # _Michael S. Branicky_, May 27 2024
%o (PARI) a(n) = my(k=2, d=Set(digits(n))); while(setintersect(Set(digits(n^k)), d) != d, k++); k; \\ _Michel Marcus_, Jun 01 2024
%Y Cf. A045537, A111442, A253600.
%K nonn,base
%O 0,1
%A _James C. McMahon_, May 27 2024
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