login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A245326 Denominators of an enumeration system of the reduced nonnegative rational numbers 15
1, 2, 1, 3, 3, 2, 1, 5, 4, 5, 4, 3, 3, 2, 1, 8, 7, 7, 5, 8, 7, 7, 5, 5, 4, 5, 4, 3, 3, 2, 1, 13, 11, 12, 9, 11, 10, 9, 6, 13, 11, 12, 9, 11, 10, 9, 6, 8, 7, 7, 5, 8, 7, 7, 5, 5, 4, 5, 4, 3, 3, 2, 1, 21, 18, 19, 14, 19, 17, 16, 11, 18, 15, 17, 13, 14, 13, 11, 7, 21, 18, 19, 14, 19, 17, 16, 11, 18, 15, 17, 13, 14, 13, 11, 7, 13, 11, 12, 9, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A245325(n)/a(n) enumerates all the reduced nonnegative rational numbers exactly once.

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, 3, 2,1,

5, 4, 5,4, 3, 3,2,1,

8, 7, 7,5, 8, 7,7,5, 5, 4, 5,4, 3, 3,2,1,

13,11,12,9,11,10,9,6,13,11,12,9,11,10,9,6,8,7,7,5,8,7,7,5,5,4,5,4,3,3,2,1,

then the sum of the m-th row is 3^m (m = 0,1,2,), and each column k is a Fibonacci sequence. These Fibonacci sequences are equal to Fibonacci sequences from A.... except the first terms of those sequences.

If the rows are written in a right-aligned fashion:

                                                                        1,

                                                                      2,1,

                                                                  3,3,2,1,

                                                          5,4,5,4,3,3,2,1,

                                          8,7,7,5,8,7,7,5,5,4,5,4,3,3,2,1,

13,11,12,9,11,10,9,6,13,11,12,9,11,10,9,6,8,7,7,5,8,7,7,5,5,4,5,4,3,3,2,1,

then each column is constant and the terms are from A071585 ( a(2^m-1-k) = A071585(k) , k = 0,1,2,...).

If the sequence is considered by blocks of length 2^m, m = 0,1,2,..., the blocks of this sequence are permutations of terms of blocks from A002487 (Stern's diatomic series or Stern-Brocot sequence), and, more precisely, the reverses of blocks of A071766 ( a(2^m+k) = A071766(2^(m+1)-1-k), m = 0,1,2,..., k = 0,1,2,...,2^m-1). Moreover, each block is the bit-reversed permutation of the corresponding block of A245328.

LINKS

Table of n, a(n) for n=1..100.

Index entries for fraction trees

PROG

(R)

blocklevel <- 6 # arbitrary

a <- 1

for(m in 0:blocklevel) for(k in 0:(2^(m-1)-1)){

  a[2^(m+1)+k]             <- a[2^m+k] + a[2^m+2^(m-1)+k]

  a[2^(m+1)+2^(m-1)+k]     <- a[2^(m+1)+k]

  a[2^(m+1)+2^m+k]         <- a[2^m+k]

  a[2^(m+1)+2^m+2^(m-1)+k] <- a[2^m+2^(m-1)+k]

}

a

CROSSREFS

Cf. A245325, A002487, A071585, A071766, A273494.

Sequence in context: A262209 A047679 A179480 * A241534 A035050 A198790

Adjacent sequences:  A245323 A245324 A245325 * A245327 A245328 A245329

KEYWORD

nonn,frac

AUTHOR

Yosu Yurramendi, Jul 18 2014

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 23 02:33 EST 2019. Contains 319365 sequences. (Running on oeis4.)