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A236673 Exponents of powers of 3 that contain all ten decimal digits.

%I A236673 #23 May 22 2025 10:21:36
%S A236673 39,45,47,48,53,57,60,61,62,63,64,65,67,69,70,71,72,73,74,76,77,78,79,
%T A236673 80,82,83,85,86,87,88,89,90,92,93,94,95,96,97,98,99,102,103,105,107,
%U A236673 108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123
%N A236673 Exponents of powers of 3 that contain all ten decimal digits.
%C A236673 It is conjectured that after a(43), a(n) = n + 63 (i.e., natural numbers beginning with 107).
%C A236673 Complement of A236674.
%H A236673 Seiichi Manyama, <a href="/A236673/b236673.txt">Table of n, a(n) for n = 1..10000</a>
%e A236673 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 A236673 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 A236673 58 is not in the sequence because there are no 5's in 3^58 = 4710128697246244834921603689.
%t A236673 Select[Range[0, 200], Union[IntegerDigits[3^#]] == Range[0, 9] &] (* _T. D. Noe_, Jan 29 2014 *)
%o A236673 (Python)
%o A236673 def PanDig(x):
%o A236673   a = '1234567890'
%o A236673   for n in range(10**3):
%o A236673     count = 0
%o A236673     for i in a:
%o A236673       if str(x**n).count(i) > 0:
%o A236673         count += 1
%o A236673       else:
%o A236673         break
%o A236673     if count == len(a):
%o A236673       print(n)
%Y A236673 Cf. A130694, A236674.
%K A236673 nonn,base
%O A236673 1,1
%A A236673 _Derek Orr_, Jan 29 2014