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A152975 Numerators of the redundant Stern-Brocot structure; denominators=A152976. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A087818 A112746 A107460 * A244758 A230493 A128262

Adjacent sequences:  A152972 A152973 A152974 * A152976 A152977 A152978

KEYWORD

frac,nonn,tabf

AUTHOR

Reinhard Zumkeller, Dec 22 2008

STATUS

approved

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Last modified December 10 11:39 EST 2016. Contains 279001 sequences.