A272826 Cubes whose digits are powers of 2.

1, 8, 21811182184

Offset

1,2

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

Links

Table of n, a(n) for n=1..3.

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A108067 A067486 A068742 * A019440 A085276 A226121

Adjacent sequences: A272823 A272824 A272825 * A272827 A272828 A272829

Keyword

nonn,bref,more,base

Author

Waldemar Puszkarz, May 07 2016

Status

approved