Friday, May 31, 2024

A373203 Contribution to the OEIS

 

A373203nulla(n) = minimum k>1 such that n^k contains all distinct decimal digits of n.0
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 (listgraphrefslistenhistoryedittextinternal format)
OFFSET
0,1
LINKS
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
CROSSREFS
Sequence in context: A005177 A357123 A253600 * A045537 A243941 A161622
KEYWORD
nonn,base,new
AUTHOR
James C. McMahon, May 27 2024
STATUS
approved

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