cp's OEIS Frontend

A057432 Obtained by reading first the numerator then the denominator of fractions in left-hand half of Stern-Brocot tree (A007305/A007306).

%I A057432 #20 Aug 13 2025 23:15:09
%S A057432 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,
%T A057432 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,
%U A057432 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
%N A057432 Obtained by reading first the numerator then the denominator of fractions in left-hand half of Stern-Brocot tree (A007305/A007306).
%H A057432 N. J. A. Sloane, <a href="/stern_brocot.html">Stern-Brocot or Farey Tree</a>
%H A057432 <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%e A057432 The tree begins:
%e A057432                                      1/1
%e A057432                                      1/2
%e A057432                   1/3                                   2/3
%e A057432         1/4                 2/5               3/5                 3/4
%e A057432     1/5      2/7       3/8       3/7     4/7       5/8       5/7      4/5
%e A057432   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
%t A057432 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]]]]]
%t A057432 Flatten[Append[{1,1},Table[Map[First,sbt[i]],{i,1,6}]]] (* _Peter Luschny_, Apr 27 2009 *)
%Y A057432 Cf. A007305, A047679, A007306, A002487, A057431.
%Y A057432 Related to the Kepler tree A294442 via row permutations given by A088208 or A131271.
%K A057432 nonn,easy,tabf
%O A057432 0,4
%A A057432 _N. J. A. Sloane_, Sep 08 2000
%E A057432 More terms from _Alford Arnold_, Sep 11 2000
%E A057432 More terms from _Joshua Zucker_, May 11 2006