A373203 - OEIS

%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