A215676 a(1) = 1, a(n) = 2 if 1

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, 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

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, A215674, A215675.

Programs

Maple

a:= proc(n) option remember; 1+ `if`(n=1, 0, `if`(n<=4, 1,
      `if`(irem(n-1, 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] = 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;
Table[a[n], {n, 1, 80}] (* Jean-François Alcover, Sep 01 2022 *)