A057432 Obtained by reading first the numerator then the denominator of fractions in left-hand half of Stern-Brocot tree (A007305/A007306).

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

Offset: 0

Author

N. J. A. Sloane, Sep 08 2000

Keywords

• nonn
• easy
• tabf

Examples

			The tree begins:
                                     1/1
                                     1/2
                  1/3                                   2/3
        1/4                 2/5               3/5                 3/4
    1/5      2/7       3/8       3/7     4/7       5/8       5/7      4/5
  1/6 2/9 3/11 3/10 4/11 5/13 5/12 4/9 5/9 7/12 8/13 7/11 7/10 8/11 7/9 5/6
		

Links

• N. J. A. Sloane, Stern-Brocot or Farey Tree
• Index entries for sequences related to Stern's sequences

Crossrefs

Cf. A007305, A047679, A007306, A002487, A057431.

Related to the Kepler tree A294442 via row permutations given by A088208 or A131271.

Programs

Mathematica

sbt[n_]:=Module[{P,L,Y},P={{1,0},{1,1}};L={{1,1},{0,1}};Y={{1,0},{0,1}}; w[b_]:=Fold[ #1.If[ #2==0,L,P]&,Y,b]; u[a_]:={a[[2,1]]+a[[2,2]],a[[1,1]]+a[[1,2]]}; s[l_]:={l,{Last[l],First[l]}}; Map[s,Map[u,Map[w,Part[Partition[Tuples[{0,1},n],2^(n-1)],1]]]]]
Flatten[Append[{1,1},Table[Map[First,sbt[i]],{i,1,6}]]] (* Peter Luschny, Apr 27 2009 *)

Extensions

More terms from Alford Arnold, Sep 11 2000

More terms from Joshua Zucker, May 11 2006