

A130693


Powers of 2 whose digits are powers of 2.


2




OFFSET

1,2


COMMENTS

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, 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, Apr 05 2008


REFERENCES

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


LINKS



MAPLE

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


MATHEMATICA

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 *)


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



