%I #21 Apr 08 2020 00:02:05

%S 39,45,47,48,53,57,60,61,62,63,64,65,67,69,70,71,72,73,74,76,77,78,79,

%T 80,82,83,85,86,87,88,89,90,92,93,94,95,96,97,98,99,102,103,105,107,

%U 108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123

%N Exponents of powers of 3 that contain all ten decimal digits.

%C It is conjectured that after a(43), a(n) = n + 63 (i.e., natural numbers beginning with 107).

%C Complement of A236674.

%H Seiichi Manyama, <a href="/A236673/b236673.txt">Table of n, a(n) for n = 1..10000</a>

%e 3^53 = 19383245667680019896796723, which contains two 1's, two 2's, three 3's, one 4, one 5, five 6's, three 7's, three 8's, four 9's and two 0's, so 53 is in the sequence.

%e 3^57 = 1570042899082081611640534563, which contains four 1's, two 2's, two 3's, three 4's, three 5's, three 6's, one 7, three 8's, two 9's and five 0's.

%e 58 is not in the sequence because there are no 5's in 3^58 = 4710128697246244834921603689.

%t Select[Range[0, 200], Union[IntegerDigits[3^#]] == Range[0, 9] &] (* _T. D. Noe_, Jan 29 2014 *)

%o (Python)

%o def PanDig(x):

%o ..a = '1234567890'

%o ..for n in range(10**3):

%o ....count = 0

%o ....for i in a:

%o ......if str(x**n).count(i) > 0:

%o ........count += 1

%o ......else:

%o ........break

%o ....if count == len(a):

%o ......print(n)

%Y Cf. A130694, A236674.

%K nonn,base

%O 1,1

%A _Derek Orr_, Jan 29 2014