

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).


LINKS



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



KEYWORD

nonn,base


AUTHOR



STATUS

approved



