A005352 Base -2 representation of -n reinterpreted as binary.

3, 2, 13, 12, 15, 14, 9, 8, 11, 10, 53, 52, 55, 54, 49, 48, 51, 50, 61, 60, 63, 62, 57, 56, 59, 58, 37, 36, 39, 38, 33, 32, 35, 34, 45, 44, 47, 46, 41, 40, 43, 42, 213, 212, 215, 214, 209, 208, 211, 210, 221, 220, 223, 222, 217, 216, 219, 218, 197, 196, 199, 198, 193, 192, 195, 194, 205, 204, 207, 206, 201, 200

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• nice
• look

Examples

			a(4) = 12 because the negabinary representation of -4 is 1100, and in ordinary binary that is 12.
a(5) = 15 because the negabinary representation of -5 is 1111, and in binary that is 15.
		

References

• M. Gardner, Knotted Doughnuts and Other Mathematical Entertainments. Freeman, NY, 1986, p. 101.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Joerg Arndt, Table of n, a(n) for n = 1..1000
• Joerg Arndt, Matters Computational (The Fxtbook), p. 58-59.
• Eric Weisstein's World of Mathematics, Negabinary
• A. Wilks, Email, May 22 1991

Crossrefs

Complement of A005351 in natural numbers.

Cf. A212529.

Programs

Haskell

a005352 = a005351 . negate  -- Reinhard Zumkeller, Feb 05 2014

Mathematica

(* This function comes from the Weisstein page *)
Negabinary[n_Integer] := Module[{t = (2/3)(4^Floor[Log[4, Abs[n] + 1] + 2] - 1)}, IntegerDigits[BitXor[n + t, t], 2]];
Table[FromDigits[Negabinary[n], 2], {n, -1, -50, -1}]
(* Alonso del Arte, Apr 04 2011 *)

PARI

a(n) = my(t=(32*4^logint(n+1,4)-2)/3); bitxor(t-n, t); \\ Ruud H.G. van Tol, Oct 19 2023

Python

def A005352(n):
    return ((b:=(4 << (n.bit_length() | 1)) // 3) - n)^b # Adrienne Leonardo, Feb 03 2025

Formula

a(n) = A005351(-n). - Reinhard Zumkeller, Feb 05 2014