A272826 - OEIS

%I #22 May 19 2016 00:51:03

%S 1,8,21811182184

%N Cubes whose digits are powers of 2.

%C Intersection of A028846 and A000578.

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

%C 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.

%C Probably this sequence is finite; further terms have at least 31 digits. - _Charles R Greathouse IV_, May 19 2016

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

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

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

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

%K nonn,bref,more,base

%O 1,2

%A _Waldemar Puszkarz_, May 07 2016