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A065674 Positions of the elements of the quasicyclic group Z+(2a+1)/(2^b) [a > 0 and a < 2^(b-1), b > 0] at the ]0,1[ side of the Stern-Brocot Tree (A007305/A007306).

%I A065674 #16 Sep 09 2023 18:02:45
%S A065674 1,4,7,64,10,13,127,16384,67,79,46,49,112,124,32767,1073741824,2050,
%T A065674 262,139,151,2560,352,766,769,415,3583,232,244,505,4093,2147483647,
%U A065674 4611686018427387904,4194307,32776,16447,16639,1057,34816,571,583,310
%N A065674 Positions of the elements of the quasicyclic group Z+(2a+1)/(2^b) [a > 0 and a < 2^(b-1), b > 0] at the ]0,1[ side of the Stern-Brocot Tree (A007305/A007306).
%H A065674 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a065/A065674.java">Java program</a> (github)
%H A065674 <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%e A065674 The fraction 1/2 is at the root (position 1), 1/4 is the left child of its left child, in the position 4 (when the tree is traversed in left-to-right, breadth-first fashion), while 3/4 is the right child of the right child of the root (pos. 7), 1/8 is at the position 64 (6 steps down the left branch from the root) and 3/8 is the right child of the left child of the root, at the position 10, etc.
%p A065674 QuasiCyclics2_pos_in_0_1_SB_tree := proc(t) local num,den; den := 2^(1+floor_log_2(t)); num := (2*(t-(den/2)))+1; RETURN(frac2position_in_0_1_SB_tree(num/den)); end;
%p A065674 [seq(QuasiCyclics2_pos_in_0_1_SB_tree(j), j=1..128)]
%p A065674 # For missing Maple functions follow A065658.
%Y A065674 Permutation of A065810. Cf. A065658, A065675.
%K A065674 nonn
%O A065674 1,2
%A A065674 _Antti Karttunen_, Nov 22 2001