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

Author

Benjamin Przybocki, May 04 2016

Keywords

• nonn
• base

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

Crossrefs

Cf. A000290, A030101, A029983, A229687.

Cf. A061457 (analogous in base 10).

Programs

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 *)

PARI

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