A057432 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Table of n, a(n) for n=0..92.

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

Index entries for sequences related to Stern's sequences

EXAMPLE

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

MATHEMATICA

Contribution from Peter Luschny, Apr 27 2009: (Start)

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, 5}]]] (End)

CROSSREFS

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

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

Sequence in context: A057940 A097285 A372917 * A374741 A361942 A302295

Adjacent sequences: A057429 A057430 A057431 * A057433 A057434 A057435

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Sep 08 2000

EXTENSIONS

More terms from Alford Arnold, Sep 11 2000

More terms from Joshua Zucker, May 11 2006

STATUS

approved