A163618 - OEIS

%I #11 Jul 31 2017 03:30:53

%S 0,1,2,1,4,1,2,5,8,1,2,1,4,9,10,13,16,1,2,1,4,1,2,5,8,17,18,17,20,25,

%T 26,29,32,1,2,1,4,1,2,5,8,1,2,1,4,9,10,13,16,33,34,33,36,33,34,37,40,

%U 49,50,49,52,57,58,61,64,1,2,1,4,1,2,5,8,1,2,1,4,9,10,13,16,1,2,1,4,1,2,5,8,17

%N a(2*n) = 2 * a(n). a(2*n - 1) = 2 * a(n) - 2 - (-1)^n, for all n in Z.

%C Integers n>=0 such that a(n) = 1 is A118113.

%C Fibbinary numbers (A003714) give all integers n>=0 for which a(n+1) = 1 or 2. - _Michael Somos_, Feb 21 2016

%H G. C. Greubel, <a href="/A163618/b163618.txt">Table of n, a(n) for n = 0..5000</a>

%F a(n) = -A163617(-n) for all n in Z.

%e G.f. = x + 2*x^2 + x^3 + 4*x^4 + x^5 + 2*x^6 + 5*x^7 + 8*x^8 + x^9 + 2*x^10 + ...

%t Table[(-1)*BitOr[-n, -2*n], {n, 0, 50}] (* _G. C. Greubel_, Jul 30 2017 *)

%o (PARI) {a(n) = n=-n; -bitor(n, n<<1)};

%o (PARI) {a(n) = if( n==0 || n==1, n, 2 * a((n+1) \ 2) - (n%2) * (2 + (-1)^((n+1) \ 2)))};

%Y Cf. A163617.

%K nonn

%O 0,3

%A _Michael Somos_, Aug 01 2009