A373203 a(n) = minimum k>1 such that n^k contains all distinct decimal digits of n.

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, 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, 4, 5, 5, 3, 3, 3, 2, 3, 2, 5, 5, 5, 5

Offset: 0

Author

James C. McMahon, May 27 2024

Keywords

• nonn
• base

Examples

			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.
		

Links

• Michel Marcus, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A045537, A111442, A253600.

Programs

Mathematica

seq={}; Do[k=1;Until[ContainsAll[IntegerDigits[n^k],IntegerDigits[n] ],k++];AppendTo[seq,k] ,{n,0,80}];seq

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

Python

from itertools import count
def a(n):
    s = set(str(n))
    return next(k for k in count(2) if s <= set(str(n**k)))
print([a(n) for n in range(81)]) # Michael S. Branicky, May 27 2024

Formula

A253600(n) <= a(n) <= A045537(n). - Michael S. Branicky, May 28 2024

A111442(n) = n^a(n).