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A215673 a(1) = 1, a(2n) = a(n)+1, a(2n+1) = a(n)+a(n+1)+1.

%I A215673 #17 Jun 16 2018 13:45:07
%S A215673 1,2,4,3,7,5,8,4,11,8,13,6,14,9,13,5,16,12,20,9,22,14,20,7,21,15,24,
%T A215673 10,23,14,19,6,22,17,29,13,33,21,30,10,32,23,37,15,35,21,28,8,29,22,
%U A215673 37,16,40,25,35,11,34,24,38,15,34,20,26,7,29,23,40,18,47,30
%N A215673 a(1) = 1, a(2n) = a(n)+1, a(2n+1) = a(n)+a(n+1)+1.
%C A215673 In the S.-H. Cha reference this is function fog_2(n).
%H A215673 Alois P. Heinz, <a href="/A215673/b215673.txt">Table of n, a(n) for n = 1..8192</a>
%H A215673 S.-H. Cha, <a href="http://csis.pace.edu/~scha/IS/FOGKN.pdf">On Parity based Divide and Conquer Recursive Functions</a>, International Conference on Computer Science and Applications, San Francisco, USA, 24-26 October 2012
%p A215673 a:= proc(n) option remember; 1+ `if`(n=1, 0,
%p A215673       `if`(irem(n, 2, 'r')=0, a(r), a(r)+a(r+1)))
%p A215673     end:
%p A215673 seq(a(n), n=1..80);  # _Alois P. Heinz_, Aug 23 2012
%t A215673 a[1] = 1;
%t A215673 a[n_] := a[n] = If[EvenQ[n], a[n/2] + 1, a[(n-1)/2] + a[(n-1)/2 + 1] + 1];
%t A215673 Array[a, 80] (* _Jean-François Alcover_, Jun 16 2018 *)
%Y A215673 Cf. A215674, A215675, A215676.
%K A215673 nonn
%O A215673 1,2
%A A215673 _Sung-Hyuk Cha_, Aug 20 2012