
COMMENTS

a(n)/A245326(n) enumerates all the reduced nonnegative rational numbers exactly once.
If the terms (n>0) are written as an array (leftaligned fashion) with rows of length 2^m, m = 0,1,2,3,...
1,
1,2,
2,1,3,3,
3,3,2,1,5,4,5,4,
5,4,5,4,3,3,2,1,8,7,7,5,8,7,7,5,
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,
then the sum of the mth row is 3^m (m = 0,1,2,), each column k is a Fibonacci sequence.
If the rows are written in a rightaligned fashion:
1,
1,2,
2, 1,3,3,
3, 3, 2,1, 5, 4,5,4,
5, 4, 5,4, 3, 3,2,1, 8, 7, 7,5, 8, 7,7,5,
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,
then each column is an arithmetic sequence. The differences of the arithmetic sequences gives the sequence A071585 (a(2^(m+1)1k)  a(2^m1k) = A071585(k), m = 0,1,2,..., k = 0,1,2,...,2^m1).
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 SternBrocot sequence), and, more precisely, the reverses of blocks of A229742 ( a(2^m+k) = A229742(2^(m+1)1k), m = 0,1,2,..., k = 0,1,2,...,2^m1). Moreover, each block is the bitreversed permutation of the corresponding block of A245327.
