A005352 Base -2 representation of -n reinterpreted as binary. (Formerly M2259)

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

1,1

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

Formula

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

Example

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.

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 *)

Prog

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

Crossrefs

Complement of A005351 in natural numbers.

Cf. A212529.

Sequence in context: A219374 A084416 A210604 * A095131 A060149 A059374

Adjacent sequences: A005349 A005350 A005351 * A005353 A005354 A005355

Keyword

nonn,base,nice,look

Author

N. J. A. Sloane

Status

approved