A130696 - OEIS

%I #38 Jul 13 2021 19:42:38

%S 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,

%T 26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,

%U 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

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

%C 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.

%C There are no more terms less than 10^10. - _David Radcliffe_, Apr 11 2019

%e 20 is in this list because 2^20 = 1048576, which doesn't contain all ten digits.

%e 68 is the first number not in this list; 2^68 = 295147905179352825856 and this contains all ten digits.

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

%t Select[Range[10^6]-1,MemberQ[DigitCount[2^#],0]&] (* _Hans Rudolf Widmer_, Jun 23 2021 *)

%o (Python) print([n for n in range(1000) if len(set(str(2**n))) < 10]) # _David Radcliffe_, Apr 11 2019

%o (PARI) hasalldigits(n) = #vecsort(digits(n), , 8)==10

%o is(n) = !hasalldigits(2^n) \\ _Felix Fröhlich_, Apr 11 2019

%Y Cf. A007377, A062518, A090493.

%Y Complement of A130694.

%K base,nonn

%O 1,3

%A _Greg Dresden_, Jul 10 2007

%E a(1) = 0 prepended by _David Radcliffe_, Apr 11 2019