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A215676 a(1) = 1, a(n) = 2 if 1 a(3n+1) = a(n)+1, a(3n+2) = a(3n+3) = a(n)+a(n+1)+1 otherwise.

%I A215676 #18 Sep 01 2022 06:01:57
%S A215676 1,2,2,2,4,4,3,5,5,3,5,5,3,7,7,5,9,9,5,8,8,4,9,9,6,11,11,6,9,9,4,9,9,
%T A215676 6,11,11,6,9,9,4,11,11,8,15,15,8,13,13,6,15,15,10,19,19,10,15,15,6,14,
%U A215676 14,9,17,17,9,13,13,5,14,14,10,19,19,10,16,16,7
%N A215676 a(1) = 1, a(n) = 2 if 1<n<=4, a(3n+1) = a(n)+1, a(3n+2) = a(3n+3) = a(n)+a(n+1)+1 otherwise.
%C A215676 In the S.-H. Cha reference this is function ~fog_3(n).
%H A215676 Alois P. Heinz, <a href="/A215676/b215676.txt">Table of n, a(n) for n = 1..8192</a>
%H A215676 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 A215676 a:= proc(n) option remember; 1+ `if`(n=1, 0, `if`(n<=4, 1,
%p A215676       `if`(irem(n-1, 3, 'r')=0, a(r), a(r)+a(r+1))))
%p A215676     end:
%p A215676 seq (a(n), n=1..80);  # _Alois P. Heinz_, Aug 23 2012
%t A215676 a[n_] := a[n] = Switch[n, 1, 0, 2|3|4, 1, _, {q, r} = QuotientRemainder[n-1, 3]; If[r == 0, a[q], a[q]+a[q+1]]]+1;
%t A215676 Table[a[n], {n, 1, 80}] (* _Jean-François Alcover_, Sep 01 2022 *)
%Y A215676 Cf. A215673, A215674, A215675.
%K A215676 nonn
%O A215676 1,2
%A A215676 _Sung-Hyuk Cha_, Aug 20 2012