A214972 a(n) = a(floor(2*(n-1)/3)) + 1, where a(0) = 0.

0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9

Offset: 0

Author

Clark Kimberling, Oct 19 2012

Keywords

• nonn

Examples

			a(10) = a(9*2/3)+1 = a(6)+1 = 3+1 = 4.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 0..10000

Programs

Mathematica

a[0] := 0; a[n_] := a[Floor[2*(n-1)/3]] + 1; Table[a[n], {n, 0, 120}]

Maxima

a[0]:0$
a[n]:=a[floor(2*(n-1)/3)] + 1$
A214972(n):=a[n];
makelist(A214972(n),n,0,30); /* Martin Ettl, Oct 31 2012 */

PARI

a214972(n) = {local(nn,r); nn=n; r=0; while(nn>0, r=r+1; nn=floor(2*(nn-1)/3)); r} \\ Michael B. Porter, Oct 30 2012

Formula

Conjecture: a(n) = a(n-1) + 1 if n is in A152009, and a(n) = a(n-1) otherwise.