A309007 Largest k such that n^k has distinct digits in base 10 (for n>1).

29, 9, 10, 8, 4, 8, 5, 3, 1, 0, 4, 4, 5, 1, 5, 6, 4, 3, 1, 3, 3, 4, 3, 4, 1, 3, 2, 3, 1, 2, 4, 2, 1, 3, 2, 2, 5, 1, 1, 3, 2, 2, 4, 1, 1, 1, 4, 4, 1, 2, 2, 2, 2, 2, 1, 2, 1, 3, 1, 2, 1, 1, 2, 1, 3, 1, 1, 3, 1, 2, 2, 3, 2, 3, 3, 0, 2, 2, 1, 1, 2, 1, 3, 1, 2, 2

Offset: 2

Author

Tom Bryan, Jul 05 2019

Keywords

• nonn
• base

Examples

			For n = 2, 2^29 = 536870912, which is the largest power of 2 to contain distinct digits.
		

Crossrefs

Cf. A010784.

For n=2, see A084688 and A260814.

Programs

Mathematica

a[n_] := SelectFirst[ Range[ Floor@ Log[n, 10^10], 0, -1], (Sort[#] == Union[#]) &@ IntegerDigits[ n^#] &]; Array[a, 86, 2] (* Giovanni Resta, Jul 07 2019 *)

PARI

a(n) = forstep (k=logint(10^10, n), 0, -1, my (d=digits(n^k)); if (#d==#Set(d), return (k))) \\ Rémy Sigrist, Jul 06 2019

Python

def distinct_digits(n):
    p = math.floor(math.log(10**10)/math.log(n))
    while p >= 1:
        d = n**p
        if len(set(str(d))) == len(str(d)):
            return(p)
        else:
            p = p - 1
    return(0)

Formula

a(n) = 0 for any n > 9876543210. - Rémy Sigrist, Jul 06 2019

Extensions

More terms from Rémy Sigrist, Jul 06 2019