

A236673


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


5



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
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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



