A260814 -id:A260814 - cp's OEIS frontend

A084688 Nonnegative integers n such that 2^n uses only distinct decimal digits.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 29

Offset: 1

Zak Seidov, Jul 01 2003

There are exactly 18 numbers such that 2^n uses only distinct digits.
a(n) can have at most 10 digits. As 2^34 has 11 digits, a(n) < 34. - David A. Corneth, Aug 03 2015
Subsequence of A052060. - R. J. Mathar, Sep 17 2008

			29 is the last term with 2^29 = 536870912 = A260814(18). - _Zak Seidov_, Aug 02 2015

Cf. A000079, A260814, A052060.

Select[Range[0, 34], Max@ DigitCount[2^#] == 1 &] (* Michael De Vlieger, Aug 03 2015 *) (* with corrections by Zak Seidov, Aug 05 2015 *)

lista() = {lim = ceil(log(10^11)/(log(2)));for (n=0, lim, d = digits(2^n); if (#vecsort(d,,8) == #d, print1(n, ", ")););} \\ Michel Marcus, Aug 03 2015

a(n) = log_2(A260814(n)). - Zak Seidov, Aug 02 2015

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

Original entry on oeis.org

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

Tom Bryan, Jul 05 2019

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

Cf. A010784.

For n=2, see A084688 and A260814.

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

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

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)

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

More terms from Rémy Sigrist, Jul 06 2019

cp's OEIS Frontend

A084688 Nonnegative integers n such that 2^n uses only distinct decimal digits.

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