A152975 - OEIS

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

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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]