A272711 Square numbers whose binary reversal is also square.

1, 4, 9, 16, 36, 64, 144, 256, 576, 1024, 2304, 4096, 9216, 16384, 36864, 65536, 147456, 262144, 589824, 1048576, 2359296, 4194304, 9437184, 16777216, 20457529, 37748736, 67108864, 81830116, 143784081, 150994944, 268435456, 327320464, 331130809, 575136324, 603979776

Offset

1,2

Comments

The first term in this sequence whose binary reversal is not 1 or 9 is 20457529 (which is a binary palindrome).

The previous comment means that the sequence does not just contain the squares of numbers in A029744. - R. J. Mathar, May 06 2016

If k is a term, then so is 4*k. - Robert Israel, Jun 06 2023

Links

Robert Israel, Table of n, a(n) for n = 1..176

Maple

rev:= proc(n) local L, i;
  L:= convert(n, base, 2);
  add(L[-i]*2^(i-1), i=1..nops(L))
end proc:
select(n -> issqr(rev(n)), [seq(i^2, i=1..100000)]); # Robert Israel, Jun 06 2023

Mathematica

Select[Range[10^5]^2, IntegerQ@ Sqrt@ FromDigits[ Reverse@ IntegerDigits[#, 2], 2] &] (* Giovanni Resta, May 05 2016 *)

Prog

(PARI) lista(nn) = {for (n=1, nn, if (issquare(subst(Polrev(binary(n^2)), x, 2)), print1(n^2, ", ")); ); } \\ Michel Marcus, May 05 2016

Crossrefs

Cf. A000290, A030101, A029983, A229687.

Cf. A061457 (analogous in base 10).

Sequence in context: A117218 A226076 A357753 * A356880 A018228 A204503

Adjacent sequences: A272708 A272709 A272710 * A272712 A272713 A272714

Keyword

nonn,base

Author

Benjamin Przybocki, May 04 2016

Status

approved