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 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 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: A324338 A047679 A179480 * A241534 A337137 A035050 Adjacent sequences:  A245323 A245324 A245325 * A245327 A245328 A245329 KEYWORD nonn,frac AUTHOR Yosu Yurramendi, Jul 18 2014 STATUS approved

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Last modified September 28 10:48 EDT 2021. Contains 347714 sequences. (Running on oeis4.)