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

0,1

Links

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

Formula

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

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

Example

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.

Mathematica

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

Prog

(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
(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

Crossrefs

Cf. A045537, A111442, A253600.

Sequence in context: A005177 A357123 A253600 * A045537 A243941 A161622

Adjacent sequences: A373200 A373201 A373202 * A373204 A373205 A373206

Keyword

nonn,base

Author

James C. McMahon, May 27 2024

Status

approved