A153161 - OEIS

%I #6 Mar 30 2012 18:51:00

%S 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,

%T 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,

%U 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

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

%C 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;

%C 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)).

%H <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>

%H N. J. A. Sloane, <a href="/stern_brocot.html">Stern-Brocot or Farey Tree</a>

%e {1/3} . . . . . . . . . . . . . . . . . . . . . . . {2/3}

%e .......................... 1/2 ..........................

%e ............... 2/5 ................. 3/5 ...............

%e ...... 3/8 .......... 3/7 ..... 4/7 .......... 5/8 ......

%e .. 4/11 .. 5/13 . 5/12 . 4/9 5/9 . 7/12 . 8/13 .. 7/11 .

%Y A007305.

%K frac,nonn,tabf

%O 1,2

%A _Reinhard Zumkeller_, Dec 22 2008