a(n)/
A245328(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,
1, 2,
2, 3,1, 3,
3, 5,2, 5,3, 4,1, 4,
5, 8,3, 8,5, 7,2, 7,4, 7,3, 7,4,5,1,5,
8,13,5,13,8,11,3,11,7,12,5,12,7,9,2,9,7,11,4,11,7,10,3,10,5,9,4,9,5,6,1,6,
then the sum of the m-th row is 3^m (m = 0,1,2,), and each column k is a Fibonacci sequence.
If the rows are written in a right-aligned fashion:
1,
1,2,
2,3,1,3,
3,5,2,5,3,4,1,4,
5, 8,3, 8,5, 7,2, 7,4,7,3,7,4,5,1,5,
8,13,5,13,8,11,3,11,7,12,5,12,7,9,2,9,7,11,4,11,7,10,3,10,5,9,4,9,5,6,1,6,
then each column is an arithmetic sequence.
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
A020650 ( a(2^m+k) =
A020650(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
A245325.
