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

39, 45, 47, 48, 53, 57, 60, 61, 62, 63, 64, 65, 67, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 82, 83, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 98, 99, 102, 103, 105, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123

Offset: 1

Author

Derek Orr, Jan 29 2014

Keywords

• nonn
• base

Comments

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

Complement of A236674.

Examples

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

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A130694, A236674.

Programs

Mathematica

Select[Range[0, 200], Union[IntegerDigits[3^#]] == Range[0, 9] &] (* T. D. Noe, Jan 29 2014 *)

Python

def PanDig(x):
  a = '1234567890'
  for n in range(10**3):
    count = 0
    for i in a:
      if str(x**n).count(i) > 0:
        count += 1
      else:
        break
    if count == len(a):
      print(n)