OFFSET
1,3
LINKS
R. Zumkeller, Table of n, a(n) for n = 1..10000
FORMULA
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}.
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
MAPLE
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
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
AUTHOR
Don Knuth, Mar 01 2008
EXTENSIONS
STATUS
approved