A142721 - OEIS

%I #16 Dec 07 2019 00:47:07

%S 0,2,1,5,2,6,3,11,4,12,5,13,6,14,7,23,8,24,9,25,10,26,11,27,12,28,13,

%T 29,14,30,15,47,16,48,17,49,18,50,19,51,20,52,21,53,22,54,23,55,24,56,

%U 25,57,26,58,27,59,28,60,29,61,30,62,31,95,32,96,33,97,34,98,35,99,36,100

%N An even-odd sequence: a(n) = n/2 if n is even, or a(n-1) + 2^floor(log_2(n+1)) otherwise.

%t a[0] = 0; a[n_] := a[n] = If[Mod[n, 2] == 0, n/2, a[n - 1] + 2^(Floor[Log[2, 1 + n]])]; Table[a[n], {n, 0, 100}]

%t nxt[{n_,a_}]:={n+1,If[EvenQ[n+1],(n+1)/2,a+2^Floor[Log[2,n+2]]]}; Transpose[ NestList[ nxt,{0,0},100]][[2]] (* _Harvey P. Dale_, Feb 26 2013 *)

%o (PARI) a(n)=n\2+if(n%2,2^(log(n+1.5)\log(2))) \\ _Charles R Greathouse IV_, Jan 30 2012

%K nonn,less,easy

%O 0,2

%A _Roger L. Bagula_ and _Gary W. Adamson_, Sep 27 2008