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A272711 Square numbers whose binary reversal is also square.

%I A272711 #25 Jun 07 2023 20:08:38
%S A272711 1,4,9,16,36,64,144,256,576,1024,2304,4096,9216,16384,36864,65536,
%T A272711 147456,262144,589824,1048576,2359296,4194304,9437184,16777216,
%U A272711 20457529,37748736,67108864,81830116,143784081,150994944,268435456,327320464,331130809,575136324,603979776
%N A272711 Square numbers whose binary reversal is also square.
%C A272711 The first term in this sequence whose binary reversal is not 1 or 9 is 20457529 (which is a binary palindrome).
%C A272711 The previous comment means that the sequence does not just contain the squares of numbers in A029744. - _R. J. Mathar_, May 06 2016
%C A272711 If k is a term, then so is 4*k. - _Robert Israel_, Jun 06 2023
%H A272711 Robert Israel, <a href="/A272711/b272711.txt">Table of n, a(n) for n = 1..176</a>
%p A272711 rev:= proc(n) local L,i;
%p A272711   L:= convert(n,base,2);
%p A272711   add(L[-i]*2^(i-1),i=1..nops(L))
%p A272711 end proc:
%p A272711 select(n -> issqr(rev(n)), [seq(i^2,i=1..100000)]); # _Robert Israel_, Jun 06 2023
%t A272711 Select[Range[10^5]^2, IntegerQ@ Sqrt@ FromDigits[ Reverse@ IntegerDigits[#, 2], 2] &] (* _Giovanni Resta_, May 05 2016 *)
%o A272711 (PARI) lista(nn) = {for (n=1, nn, if (issquare(subst(Polrev(binary(n^2)), x, 2)), print1(n^2, ", ")););} \\ _Michel Marcus_, May 05 2016
%Y A272711 Cf. A000290, A030101, A029983, A229687.
%Y A272711 Cf. A061457 (analogous in base 10).
%K A272711 nonn,base
%O A272711 1,2
%A A272711 _Benjamin Przybocki_, May 04 2016