

A130696


Numbers k such that 2^k does not contain all ten decimal digits.


6



0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 71, 72, 73, 74, 75, 76, 77, 78, 80, 81, 83, 85, 86, 90, 91, 92, 93, 99, 102, 107, 108, 153, 168
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OFFSET

1,3


COMMENTS

It is believed that 168 is the last number in this list; 2^168 is a 51digit number that contains all the digits except (oddly enough) 2.


LINKS



EXAMPLE

20 is in this list because 2^20 = 1048576, which doesn't contain all ten digits.
68 is the first number not in this list; 2^68 = 295147905179352825856 and this contains all ten digits.


MATHEMATICA

A2 := {}; Do[If[Length[Union[ IntegerDigits[2^ n]]] != 10, A2 = Join[A2, {n}]], {n, 1, 3000}]; Print[A2]


PROG

(Python) print([n for n in range(1000) if len(set(str(2**n))) < 10]) # David Radcliffe, Apr 11 2019
(PARI) hasalldigits(n) = #vecsort(digits(n), , 8)==10


CROSSREFS



KEYWORD

base,nonn


AUTHOR



EXTENSIONS



STATUS

approved



