A215674 a(1) = 1, a(n) = 2 if 1

1, 2, 2, 4, 4, 3, 5, 5, 3, 7, 7, 5, 9, 9, 5, 8, 8, 4, 9, 9, 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, 14, 9, 17, 17, 9, 13, 13, 5, 14, 14, 10, 19, 19, 10, 16, 16, 7, 18, 18, 12, 23, 23, 12, 18, 18, 7, 16

Offset: 1

Author

Sung-Hyuk Cha, Aug 20 2012

Keywords

• nonn

Comments

In the S.-H. Cha reference this is function fog_3(n).

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..8192
• S.-H. Cha, On Parity based Divide and Conquer Recursive Functions, International Conference on Computer Science and Applications, San Francisco, USA, 24-26 October 2012

Crossrefs

Cf. A215673, A215675, A215676.

Programs

Maple

a:= proc(n) option remember; 1+ `if`(n=1, 0, `if`(n<=3, 1,
      `if`(irem(n, 3, 'r')=0, a(r), a(r)+a(r+1))))
    end:
seq (a(n), n=1..80);  # Alois P. Heinz, Aug 23 2012

Mathematica

a[n_] := a[n] = If[n < 3, n, {q, r} = QuotientRemainder[n, 3];
     Switch[r, 0, a[q] + 1, 1|2, a[q] + a[q+1] + 1]];
Table[a[n], {n, 1, 80}] (* Jean-François Alcover, Apr 24 2022 *)