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A309007
Largest k such that n^k has distinct digits in base 10 (for n>1).
0
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
2,1
FORMULA
a(n) = 0 for any n > 9876543210. - Rémy Sigrist, Jul 06 2019
EXAMPLE
For n = 2, 2^29 = 536870912, which is the largest power of 2 to contain distinct digits.
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 *)
PROG
(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)
(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
CROSSREFS
Cf. A010784.
For n=2, see A084688 and A260814.
Sequence in context: A040818 A216709 A040817 * A070714 A040816 A336061
KEYWORD
nonn,base
AUTHOR
Tom Bryan, Jul 05 2019
EXTENSIONS
More terms from Rémy Sigrist, Jul 06 2019
STATUS
approved