This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A272826 #22 May 19 2016 00:51:03
%S A272826 1,8,21811182184
%N A272826 Cubes whose digits are powers of 2.
%C A272826 Intersection of A028846 and A000578.
%C A272826 1 and 8, as Fibonacci numbers, are also members of A272827.
%C A272826 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 A272826 Probably this sequence is finite; further terms have at least 31 digits. - _Charles R Greathouse IV_, May 19 2016
%e A272826 21811182184 is a term as its digits are only powers of 2; its cube root is 2794.
%t A272826 Select[Range[1000000]^3, SubsetQ[{1,2,4,8}, IntegerDigits@#]&]
%o A272826 (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 A272826 Cf. A000578 (cubes), A028846 (numbers whose digits are powers of 2), A272827 (related sequence).
%K A272826 nonn,bref,more,base
%O A272826 1,2
%A A272826 _Waldemar Puszkarz_, May 07 2016