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 A272884 #20 Aug 05 2024 14:22:22
%S A272884 1,4,81,121,144,441,484,841,1444,8281,11881,14884,28224,48841,114244,
%T A272884 128881,142884,221841,228484,848241,1121481,1281424,1418481,2184484,
%U A272884 2214144,8282884,11142244,11282881,18241441,18818244,18844281,21242881,21818241,28281124,82428241,121242121,121484484,124121881
%N A272884 Squares whose digits are powers of 2.
%C A272884 Intersection of A000290 and A028846.
%C A272884 Note that in contrast to this sequence, which contains 102 terms up to 10^12, the analogous sequence of cubes (A272826) may contain only 3 in total.
%C A272884 Moreover, the similar sequences for the fourth and fifth perfect powers seem to contain only two terms (1, 81) in the case of the former and only one term (1) in the case of the latter. Higher powers also appear to produce sequences with one (mostly) or two terms only.
%C A272884 Unlike the analogous sequence for cubes, this sequence is heuristically infinite. - _Charles R Greathouse IV_, May 08 2016
%C A272884 This sequence is infinite because it contains the squares of the numbers of the forms 10*(10^k-1)/3+8 and 100*(10^k-1)/3+59. - _Giovanni Resta_, May 09 2016
%C A272884 Additionally, this sequence contains the squares of the numbers of the form 1000*(10^k-1)/3 + 809 for k > 2. For k > 2, numbers of the form (1000*(10^k-1)/3 + 809)^2 contains all digits that are powers of 2. - _Altug Alkan_, May 14 2016
%H A272884 Giovanni Resta, <a href="/A272884/b272884.txt">Table of n, a(n) for n = 1..10000</a>
%e A272884 144 is a term as its digits are only powers of 2 and it is a square, 144 = 12^2.
%t A272884 Select[Range[12000]^2, SubsetQ[{1, 2, 4, 8}, IntegerDigits@#] &]
%t A272884 Select[Flatten[Table[FromDigits/@Tuples[{1,2,4,8},n],{n,9}]],IntegerQ[Sqrt[#]]&] (* _Harvey P. Dale_, Aug 05 2024 *)
%o A272884 (PARI) is(n)=issquare(n) && #setintersect(Set(digits(n)), [0,3,5,6,7,9])==0 \\ _Charles R Greathouse IV_, May 08 2016
%Y A272884 Cf. A000290 (squares), A028846 (numbers whose digits are powers of 2), A272826 (similar sequence for cubes).
%K A272884 nonn,base
%O A272884 1,2
%A A272884 _Waldemar Puszkarz_, May 08 2016