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

Author

Greg Dresden, Jul 10 2007

Keywords

• base
• nonn

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

Examples

			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.
		

Crossrefs

Cf. A007377, A062518, A090493.

Complement of A130694.

Programs

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 *)

PARI

hasalldigits(n) = #vecsort(digits(n), , 8)==10
is(n) = !hasalldigits(2^n) \\ Felix Fröhlich, Apr 11 2019

Python

print([n for n in range(1000) if len(set(str(2**n))) < 10]) # David Radcliffe, Apr 11 2019

Extensions

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