|
%I #10 Aug 08 2015 23:49:38
%S 0,1,2,2,4,5,10,3,6,7,14,8,16,17,34,4,8,9,18,10,20,21,42,11,22,23,46,
%T 24,48,49,98,5,10,11,22,12,24,25,50,13,26,27,54,28,56,57,114,14,28,29,
%U 58,30,60,61,122,31,62,63,126,64,128,129,258,6,12,13,26,14,28,29,58,15,30
%N a(1)=0; for n >= 1, a(2n)=a(n)+2^A000120(n)-1, a(2n+1)=2a(2n).
%H R. Zumkeller, <a href="/A135586/b135586.txt">Table of n, a(n) for n = 1..10000</a>
%F If n=2^{e_{k-1}}+ ... +2^{e_1}+2^{e_0}, where k=A000120(n) and e_{k-1}> ... >e_1>e_0, then a(n)=e_0+2e_1+ ... +2^{k-1}e_{k-1}.
%F a(2^k) = k; a(4*k+2) = a(4*k+1) + 1; a(4*k+3) = 2*a(4*k+2). - _Reinhard Zumkeller_, Mar 02 2008
%p b:=proc(n)if n=0 then 0 elif `mod`(n,2)=0 then b((1/2)*n) else b((1/2)*n-1/2)+1 end if end proc: a:=proc(n) if n=1 then 0 elif `mod`(n, 2)=0 then a((1/2)*n)+2^b(n)-1 else 2*a(n-1) end if end proc: seq(a(n),n=1..60); # _Emeric Deutsch_, Mar 02 2008
%t a = {0}; For[n = 2, n < 80, n++, If[OddQ[n], AppendTo[a, 2*a[[ -1]]], AppendTo[a, a[[n/2]] + 2^Length[Select[IntegerDigits[n/2, 2], # == 1 &]] - 1]]]; a (* _Stefan Steinerberger_, Mar 02 2008 *)
%Y Cf. A135587, A000120, A135533.
%K nonn,easy,look
%O 1,3
%A _Don Knuth_, Mar 01 2008
%E More terms from _Reinhard Zumkeller_, _Emeric Deutsch_ and _Stefan Steinerberger_, Mar 02 2008
|
