A152975 Numerators of the redundant Stern-Brocot structure; denominators=A152976.

1, 1, 3, 2, 1, 3, 2, 5, 3, 6, 3, 1, 3, 2, 5, 3, 6, 3, 7, 4, 9, 5, 10, 5, 9, 4, 1, 3, 2, 5, 3, 6, 3, 7, 4, 9, 5, 10, 5, 9, 4, 9, 5, 12, 7, 15, 8, 15, 7, 14, 7, 15, 8, 15, 7, 12, 5, 1, 3, 2, 5, 3, 6, 3, 7, 4, 9, 5, 10, 5, 9, 4, 9, 5, 12, 7, 15, 8, 15, 7, 14, 7, 15, 8, 15, 7, 12, 5, 11, 6, 15, 9, 20, 11, 21

Offset

1,3

Comments

The redundant Stern-Brocot structure is constructed row by row: insert between consecutive terms of the full Stern-Brocot tree their mediant (non-reduced), where the mediant of s/t and u/v = (s+u)/(t+v);

a(2^n-n+2*k) = A007305(2^(n-1)+k+2) for 0<=k<2^(n-1);

a(2^n-n+2*k-1) = A007305(2^(n-1)+k-1+2) + A007305(2^(n-1)+k+2) for 0<k<2^(n-1);

the graph of this structure describes an interesting ternary representation of the positive rational numbers;

A060188(k+2) = Sum(a(i): 2^k <= i < 2^(k+1)).

References

Milad Niqui, Formalising Exact Arithmetic, Ph.D. thesis, Radboud Universiteit Nijmegen, IPA Dissertation Series 2004-10, 2.6, p.65f .

Links

Table of n, a(n) for n=1..95.

Milad Niqui, Formalising Exact Arithmetic

Index entries for sequences related to Stern's sequences

Example

[0/1] . . . . . . . . . . . . . . . . . . . . . . . . . . . [1/0]
.............................. 1/1
............. 1/2 ............ 3/3 ............ 2/1
..... 1/3 ... 3/6 .... 2/3 ... 5/5 ... 3/2 .... 6/3 ... 3/1
. 1/4 3/9 2/5 5/10 3/5 6/9 3/4 7/7 4/3 9/6 5/3 10/5 5/2 9/3 4/1.

Crossrefs

Sequence in context: A112746 A107460 A353298 * A327439 A244758 A230493

Adjacent sequences: A152972 A152973 A152974 * A152976 A152977 A152978

Keyword

frac,nonn,tabf

Author

Reinhard Zumkeller, Dec 22 2008

Status

approved