A130696 Numbers k such that 2^k does not contain all ten decimal digits.

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

Offset

1,3

Comments

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

There are no more terms less than 10^10. - David Radcliffe, Apr 11 2019

Links

Table of n, a(n) for n=1..92.

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]
Select[Range[10^6]-1, MemberQ[DigitCount[2^#], 0]&] (* Hans Rudolf Widmer, Jun 23 2021 *)

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
is(n) = !hasalldigits(2^n) \\ Felix Fröhlich, Apr 11 2019

Crossrefs

Cf. A007377, A062518, A090493.

Complement of A130694.

Sequence in context: A090109 A153671 A090107 * A146297 A296876 A144972

Adjacent sequences: A130693 A130694 A130695 * A130697 A130698 A130699

Keyword

base,nonn

Author

Greg Dresden, Jul 10 2007

Extensions

a(1) = 0 prepended by David Radcliffe, Apr 11 2019

Status

approved