This site is supported by donations to The OEIS Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A162912 Denominators of drib tree fractions, where drib is the bit-reversal permutation tree of the Bird tree. 10
 1, 2, 1, 3, 1, 3, 2, 5, 2, 4, 3, 4, 1, 5, 3, 8, 3, 7, 5, 5, 1, 7, 4, 7, 3, 5, 4, 7, 2, 8, 5, 13, 5, 11, 8, 9, 2, 12, 7, 9, 4, 6, 5, 10, 3, 11, 7, 11, 4, 10, 7, 6, 1, 9, 5, 12, 5, 9, 7, 11, 3, 13, 8, 21, 8, 18, 13, 14, 3, 19, 11, 16, 7, 11, 9, 17, 5, 19, 12, 14, 5, 13, 9, 7, 1, 11, 6, 17, 7, 13, 10, 15 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The drib tree is an infinite binary tree labeled with rational numbers. It is generated by the following iterative process: start with the rational 1; for the left subtree increment and then take the reciprocal of the current rational; for the right subtree interchange the order of the two steps: take the reciprocal and then increment. Like the Stern-Brocot and the Bird tree, the drib tree enumerates the positive rationals: A162911(n)/A162912(n). From Yosu Yurramendi, Jul 11 2014: (Start) If the terms (n>0) are written as an array (left-aligned fashion) with rows of length 2^m, m = 0,1,2,3,... 1, 2, 1, 3, 1, 3,2, 5, 2, 4,3,4,1, 5,3, 8, 3, 7,5,5,1, 7,4,7,3,5,4, 7,2, 8,5, 13,5,11,8,9,2,12,7,9,4,6,5,10,3,11,7,11,4,10,7,6,1,9,5,12,5,9,7,11,3,13,8, then the sum of the m-th row is 3^m (m = 0,1,2,), and each column k is a Fibonacci sequence (a(2^(m+2)+k) = a(2^(m+1)+k) + a(2^m+k), m = 0,1,2,..., k = 0,1,2,...,2^m-1). If the rows are written in a right-aligned fashion:                                                                         1,                                                                       2,1,                                                                  3,1, 3,2,                                                         5,2,4,3, 4,1, 5,3,                                       8,3, 7,5,5,1,7,4, 7,3,5,4, 7,2, 8,5, 13,5,11,8,9,2,12,7,9,4,6,5,10,3,11,7,11,4,10,7,6,1,9,5,12,5,9,7,11,3,13,8, then each column k also is a Fibonacci sequence. If the sequence is considered by blocks of length 2^m, m = 0,1,2,..., the blocks of this sequence are the reverses of blocks of A162911 ( a(2^m+k) = A162911(2^(m+1)-1-k), m = 0,1,2,..., k = 0,1,2,...,2^m-1). (End) LINKS R. Hinze, Functional pearls: the bird tree, J. Funct. Programming 19 (2009), no. 5, 491-508. FORMULA b(n) where a(1) = 1; a(2n) = b(n); a(2n+1) = a(n) + b(n); and b(1) = 1; b(2n) = a(n) + b(n); b(2n+1) = a(n). a(2^(m+1)+2*k) = a(2^m+k) + a(2^(m+1)-1-k) , a(2^(m+1)+2*k+1) = a(2^(m+1)-1-k) , a(1) = 1 , m=0,1,2,3,... , k=0,1,...,2^m-1. - Yosu Yurramendi, Jul 11 2014 a(2^(m+1) + 2*k + 1) = A162911(2^m + k), m >= 0, 0 <= k < 2^m. a(2^(m+1) + 2*k) = A162911(2^m + k) + a(2^m + k), m >= 0, 0 <= k < 2^m. - Yosu Yurramendi, Mar 30 2016 a(n*2^(m+1) + A096773(m)) = A268087(n), n > 0, m >= 0.  - Yosu Yurramendi, Feb 20 2017 EXAMPLE The first four levels of the drib tree: [1/1], [1/2, 2/1], [2/3, 3/1, 1/3, 3/2], [3/5, 5/2, 1/4, 4/3, 3/4, 4/1, 2/5, 5/3]. PROG (Haskell) import Ratio; drib :: [Rational]; drib = 1 : map (recip . succ) drib \/ map (succ . recip) drib; (a : as) \/ bs = a : (bs \/ as); a162911 = map numerator drib; a162912 = map denominator drib (R) blocklevel <- 6 # arbitrary a <- 1 for(m in 0:blocklevel) for(k in 0:(2^m-1)){   a[2^(m+1)+2*k]   <- a[2^(m+1)-1-k] + a[2^m+k]   a[2^(m+1)+2*k+1] <- a[2^(m+1)-1-k] } a # Yosu Yurramendi, Jul 11 2014 CROSSREFS This sequence is the composition of A162910 and A059893: a(n) = A162910(A059893(n)). This sequence is a permutation of A002487(n+2). Cf. A096773. Sequence in context: A007735 A002616 A046073 * A230070 A224762 A039776 Adjacent sequences:  A162909 A162910 A162911 * A162913 A162914 A162915 KEYWORD easy,frac,nonn AUTHOR Ralf Hinze (ralf.hinze(AT)comlab.ox.ac.uk), Aug 05 2009 EXTENSIONS Edited by Charles R Greathouse IV, May 13 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 15 23:42 EST 2019. Contains 319184 sequences. (Running on oeis4.)