A153161 Numerators of Stern-Brocot tree hanging between 1/3 and 2/3; denominators=A153162.

1, 2, 3, 3, 3, 4, 5, 4, 5, 5, 4, 5, 7, 8, 7, 5, 7, 8, 7, 7, 8, 7, 5, 6, 9, 11, 10, 11, 13, 12, 9, 6, 9, 11, 10, 11, 13, 12, 9, 9, 12, 13, 11, 10, 11, 9, 6, 7, 11, 14, 13, 15, 18, 17, 13, 14, 19, 21, 18, 17, 19, 16, 11, 7, 11, 14, 13, 15, 18, 17, 13, 14, 19, 21, 18, 17, 19, 16, 11, 11, 16, 19

Offset

1,2

Comments

For all coprime pairs (u,v) with 1/3 < u/v < 2/3 exists a unique k such that a(k)=u and A153162(k)=v;

a(1) = 1 and for n>1: a(n) = if A025480(n-1)<>0 and A025480(n)<>0 then a(A025480(n-1))+a(A025480(n)) else if A025480(n)=0 then a(A025480(n-1))+2 else 1+a(A025480(n-1)).

Links

Table of n, a(n) for n=1..82.

Index entries for sequences related to Stern's sequences

N. J. A. Sloane, Stern-Brocot or Farey Tree

Example

{1/3} . . . . . . . . . . . . . . . . . . . . . . . {2/3}
.......................... 1/2 ..........................
............... 2/5 ................. 3/5 ...............
...... 3/8 .......... 3/7 ..... 4/7 .......... 5/8 ......
.. 4/11 .. 5/13 . 5/12 . 4/9 5/9 . 7/12 . 8/13 .. 7/11 .

Crossrefs

A007305.

Sequence in context: A134841 A071112 A097087 * A346373 A238516 A282692

Adjacent sequences: A153158 A153159 A153160 * A153162 A153163 A153164

Keyword

frac,nonn,tabf

Author

Reinhard Zumkeller, Dec 22 2008

Status

approved