A284670 Exponents of powers of 5 that contain all ten decimal digits.

19, 22, 26, 27, 28, 29, 31, 34, 35, 37, 39, 40, 41, 49, 50, 51, 52, 56, 57, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104

Offset

1,1

Comments

It is conjectured that a(n) = n + 40 for n > 25.

Links

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

Example

5^19 = 19073486328125, which contains two 1's, two 2's, two 3's, one 4, one 5, one 6, one 7, two 8's, one 9 and one 0, so 19 is in the sequence.

Mathematica

Select[Range[110], Union[IntegerDigits[5^#]] == Range[0, 9] &] (* Indranil Ghosh, Apr 01 2017 *)

Prog

(PARI) isok(n) = #vecsort(digits(5^n), , 8) == 10; \\ Michel Marcus, Apr 01 2017
(Python)
from sympy.ntheory.factor_ import digits
r10 = set(range(10))
print([n for n in range(1, 111) if set(sorted(digits(5**n)[1:])) == r10]) # Indranil Ghosh, Apr 01 2017

Crossrefs

Cf. A130694 (k=2), A236673 (k=3), this sequence (k=5).

Sequence in context: A050714 A113868 A056025 * A099954 A335347 A374465

Adjacent sequences: A284667 A284668 A284669 * A284671 A284672 A284673

Keyword

nonn,base

Author

Seiichi Manyama, Apr 01 2017

Status

approved