cp's OEIS Frontend

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

%I A152975 #5 Mar 30 2012 18:51:00
%S A152975 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,
%T A152975 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,
%U A152975 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
%N A152975 Numerators of the redundant Stern-Brocot structure; denominators=A152976.
%C A152975 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);
%C A152975 a(2^n-n+2*k) = A007305(2^(n-1)+k+2) for 0<=k<2^(n-1);
%C A152975 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);
%C A152975 the graph of this structure describes an interesting ternary representation of the positive rational numbers;
%C A152975 A060188(k+2) = Sum(a(i): 2^k <= i < 2^(k+1)).
%D A152975 Milad Niqui, Formalising Exact Arithmetic, Ph.D. thesis, Radboud Universiteit Nijmegen, IPA Dissertation Series 2004-10, 2.6, p.65f .
%H A152975 Milad Niqui, <a href="http://www.cs.ru.nl/~milad/proefschrift/thesis.pdf">Formalising Exact Arithmetic</a>
%H A152975 <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%e A152975 [0/1] . . . . . . . . . . . . . . . . . . . . . . . . . . . [1/0]
%e A152975 .............................. 1/1
%e A152975 ............. 1/2 ............ 3/3 ............ 2/1
%e A152975 ..... 1/3 ... 3/6 .... 2/3 ... 5/5 ... 3/2 .... 6/3 ... 3/1
%e A152975 . 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.
%K A152975 frac,nonn,tabf
%O A152975 1,3
%A A152975 _Reinhard Zumkeller_, Dec 22 2008