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Exponents of powers of 5 that contain all ten decimal digits.
3

%I #30 May 09 2021 09:51:36

%S 19,22,26,27,28,29,31,34,35,37,39,40,41,49,50,51,52,56,57,59,60,61,62,

%T 63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,

%U 87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104

%N Exponents of powers of 5 that contain all ten decimal digits.

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

%H Seiichi Manyama, <a href="/A284670/b284670.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%t Select[Range[110], Union[IntegerDigits[5^#]] == Range[0, 9] &] (* _Indranil Ghosh_, Apr 01 2017 *)

%o (PARI) isok(n) = #vecsort(digits(5^n),,8) == 10; \\ _Michel Marcus_, Apr 01 2017

%o (Python)

%o from sympy.ntheory.factor_ import digits

%o r10 = set(range(10))

%o print([n for n in range(1, 111) if set(sorted(digits(5**n)[1:])) == r10]) # _Indranil Ghosh_, Apr 01 2017

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

%K nonn,base

%O 1,1

%A _Seiichi Manyama_, Apr 01 2017