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

1,1

Comments

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

Complement of A236674.

Links

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

Example

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.

Mathematica

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

Prog

(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)

Crossrefs

Cf. A130694, A236674.

Sequence in context: A261374 A309696 A061756 * A119028 A252712 A252711

Adjacent sequences: A236670 A236671 A236672 * A236674 A236675 A236676

Keyword

nonn,base

Author

Derek Orr, Jan 29 2014

Status

approved