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 A130693 Powers of 2 whose digits are powers of 2. 2

%I

%S 1,2,4,8,128

%N Powers of 2 whose digits are powers of 2.

%C It is unknown if there are any other powers of 2 with this property (that is, the digits are composed only of the numbers 1,2,4,8).

%C No more powers of 2 with this property up to 2^(70000) (Saunders, J. of Recreational Mathematics, v. 26, p. 151). - _Emeric Deutsch_, Jul 15 2007

%C By looking at just the lowest 20 digits of the powers of 2, the Mathematica program shows that there are no other terms less than 2^10000000. - _T. D. Noe_, Apr 05 2008

%D David Wells, "The Penguin Dictionary of Curious and Interesting Numbers" (1997), p. 123.

%p a := proc (n) if `subset`(convert(convert(2^n, base, 10), set), {1, 2, 4, 8}) then 2^n else end if end proc: seq(a(n), n = 0 .. 300); # _Emeric Deutsch_, Jul 15 2007

%t pwr=1; Do[pwr=Mod[2*pwr,10^20]; d=Union[IntegerDigits[pwr]]; If[Intersection[d,{3,5,6,7,9,0}]=={}, Print[n]], {n,10000000}] (* _T. D. Noe_, Apr 05 2008 *)

%K nonn,base

%O 1,2

%A _Greg Dresden_, Jul 09 2007

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Last modified March 25 17:06 EDT 2023. Contains 361528 sequences. (Running on oeis4.)