1,2

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).

No more powers of 2 with this property up to 2^(70000) (Saunders, J. of Recreational Mathematics, v. 26, p. 151). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 15 2007

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 (noe(AT)sspectra.com), Apr 05 2008

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

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 (deutsch(AT)duke.poly.edu), Jul 15 2007

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 (noe(AT)sspectra.com), Apr 05 2008

Sequence in context: A018713 A007633 A018777 this_sequence A060815 A110746 A084010

Adjacent sequences: A130690 A130691 A130692 this_sequence A130694 A130695 A130696

nonn

Gregory P. Dresden (dresdeng(AT)wlu.edu), Jul 09 2007