A130693 Powers of 2 whose digits are powers of 2.

1, 2, 4, 8, 128

Offset: 1

Author

Greg Dresden, Jul 09 2007

Keywords

• nonn
• base

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.

Programs

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 *)