A104895 a(0)=0; thereafter a(2n) = -2*a(n), a(2n+1) = 2*a(n) - 1.

0, -1, -2, 1, -4, 3, 2, -3, -8, 7, 6, -7, 4, -5, -6, 5, -16, 15, 14, -15, 12, -13, -14, 13, 8, -9, -10, 9, -12, 11, 10, -11, -32, 31, 30, -31, 28, -29, -30, 29, 24, -25, -26, 25, -28, 27, 26, -27, 16, -17, -18, 17, -20, 19, 18, -19, -24, 23, 22, -23, 20, -21, -22, 21, -64, 63, 62, -63, 60, -61, -62, 61, 56, -57, -58, 57, -60, 59

Offset

0,3

Comments

Columns of table in A104894 written in base 10.

Conjecture: the positions where 0, 1, 2, 3, ... appear are given by A048724; the positions where -1, -2, -3, ... appear are given by A065621.

Links

N. J. A. Sloane, Table of n, a(n) for n = 0..20000

Formula

a(0) = 0 and for k>=0, 0<= j <2^k, a(2^k + j) = a(j) + 2^k if a(j)<0, a(2^k + j) = a(j) - 2^k if a(j)>=0.

Sum_{0 <= n <= 2^k - 1} a(n) = - 2^(k-1).

Sum_{0 <= n <= 2^k - 1} |a(n)| = 4^(k-1).

a(n) = -A065620(n). - M. F. Hasler, Apr 16 2018

Maple

f:=proc(n) option remember; if n=0 then RETURN(0); fi; if n mod 2 = 0 then RETURN(2*f(n/2)); else RETURN(-2*f((n-1)/2)-1); fi; end;

Mathematica

a[0] = 0;
a[n_]:= a[n]= If[EvenQ[n], 2 a[n/2], -2 a[(n-1)/2] - 1];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Aug 03 2018 *)

Prog

(Haskell)
import Data.List (transpose)
a104895 n = a104895_list !! n
a104895_list = 0 : concat (transpose [map (negate . (+ 1)) zs, tail zs])
               where zs = map (* 2) a104895_list
-- Reinhard Zumkeller, Mar 26 2014
(SageMath)
def a(n):
    if (n==0): return 0
    elif (mod(n, 2)==0): return 2*a(n/2)
    else: return -2*a((n-1)/2) - 1
[a(n) for n in (0..100)] # G. C. Greubel, Jun 15 2021

Crossrefs

Cf. A048724, A065621, A104894.

The negative of entry A065620.

Sequence in context: A082497 A242364 A065620 * A103122 A214918 A328394

Adjacent sequences: A104892 A104893 A104894 * A104896 A104897 A104898

Keyword

sign,look,nice

Author

Philippe Deléham, Apr 24 2005

Extensions

Corrected by N. J. A. Sloane, Nov 05 2005

Edited by N. J. A. Sloane, Apr 25 2018

Status

approved