A323066 Numbers whose binary complement (A035327) is a square.

0, 1, 2, 3, 6, 7, 11, 14, 15, 22, 27, 30, 31, 38, 47, 54, 59, 62, 63, 78, 91, 102, 111, 118, 123, 126, 127, 134, 155, 174, 191, 206, 219, 230, 239, 246, 251, 254, 255, 286, 315, 342, 367, 390, 411, 430, 447, 462, 475, 486, 495, 502, 507, 510, 511, 539, 582, 623, 662

Offset: 1

Author

Alex Ratushnyak, Jan 03 2019

Keywords

• nonn
• easy
• base

Comments

The binary complement of every square is in the sequence. Using that might ease computation. - David A. Corneth, Jan 08 2019

Examples

			The binary complement of 22 is 9. Because 9 is a square, 22 is in the sequence.
The binary complement of 4^2 = 16 is 15 so 15 is in the sequence. - _David A. Corneth_, Jan 08 2019
		

Crossrefs

Cf. A035327, A000290, A000225 is a subsequence.

Programs

Maple

q:= n-> issqr(Bits[Nand](n$2)):
select(q, [$0..1000])[];  # Alois P. Heinz, Sep 03 2021

Mathematica

Select[Range@ 700, IntegerQ@ Sqrt@ FromDigits[IntegerDigits[#, 2] /. {0 -> 1, 1 -> 0}, 2] &] (* Michael De Vlieger, Jan 04 2019 *)

PARI

bc(n) = bitxor(n, 2^(1+logint(max(n, 1), 2))-1); \\ A035327
isok(n) = issquare(bc(n)); \\ Michel Marcus, Jan 04 2019