login
Largest k such that n^k has distinct digits in base 10 (for n>1).
0

%I #28 Jul 09 2019 21:32:45

%S 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,

%T 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,

%U 3,1,2,2,3,2,3,3,0,2,2,1,1,2,1,3,1,2,2

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

%F a(n) = 0 for any n > 9876543210. - _Rémy Sigrist_, Jul 06 2019

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

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

%o (Python)

%o def distinct_digits(n):

%o p = math.floor(math.log(10**10)/math.log(n))

%o while p >= 1:

%o d = n**p

%o if len(set(str(d))) == len(str(d)):

%o return(p)

%o else:

%o p = p - 1

%o return(0)

%o (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

%Y Cf. A010784.

%Y For n=2, see A084688 and A260814.

%K nonn,base

%O 2,1

%A _Tom Bryan_, Jul 05 2019

%E More terms from _Rémy Sigrist_, Jul 06 2019