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).

1, 4, 7, 64, 10, 13, 127, 16384, 67, 79, 46, 49, 112, 124, 32767, 1073741824, 2050, 262, 139, 151, 2560, 352, 766, 769, 415, 3583, 232, 244, 505, 4093, 2147483647, 4611686018427387904, 4194307, 32776, 16447, 16639, 1057, 34816, 571, 583, 310

Offset: 1

Author

Antti Karttunen, Nov 22 2001

Keywords

• nonn

Examples

			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.
		

Links

• Sean A. Irvine, Java program (github)
• Index entries for sequences related to Stern's sequences

Crossrefs

Permutation of A065810. Cf. A065658, A065675.

Programs

Maple

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;
[seq(QuasiCyclics2_pos_in_0_1_SB_tree(j), j=1..128)]
# For missing Maple functions follow A065658.