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

Author

Seiichi Manyama, Apr 01 2017

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Mathematica

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

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