A272826 Cubes whose digits are powers of 2.

1, 8, 21811182184

Offset: 1

Author

Waldemar Puszkarz, May 07 2016

Keywords

• nonn
• bref
• more
• base

Comments

Intersection of A028846 and A000578.

1 and 8, as Fibonacci numbers, are also members of A272827.

There are many squares whose digits are powers of 2: 1,4,81,121,144, to name just a few; there are 102 of them up to 10^12. In contrast, there are very few such cubes, only 3 up to 10^18.

Probably this sequence is finite; further terms have at least 31 digits. - Charles R Greathouse IV, May 19 2016

Examples

			21811182184 is a term as its digits are only powers of 2; its cube root is 2794.
		

Crossrefs

Cf. A000578 (cubes), A028846 (numbers whose digits are powers of 2), A272827 (related sequence).

Programs

Mathematica

Select[Range[1000000]^3, SubsetQ[{1,2,4,8}, IntegerDigits@#]&]

PARI

is(n)=ispower(n,3) && #setintersect(Set(digits(n)),[0,3,5,6,7,9])==0 \\ Charles R Greathouse IV, May 08 2016