This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A245326 #34 Apr 24 2024 22:16:31
%S A245326 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,
%T A245326 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,
%U A245326 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
%N A245326 Denominators of an enumeration system of the reduced nonnegative rational numbers.
%C A245326 A245325(n)/a(n) enumerates all the reduced nonnegative rational numbers exactly once.
%C A245326 If the terms (n>0) are written as an array (in a left-aligned fashion) with rows of length 2^m, m = 0,1,2,3,...
%C A245326 1,
%C A245326 2, 1,
%C A245326 3, 3, 2,1,
%C A245326 5, 4, 5,4, 3, 3,2,1,
%C A245326 8, 7, 7,5, 8, 7,7,5, 5, 4, 5,4, 3, 3,2,1,
%C A245326 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,
%C A245326 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 for the first terms of those sequences.
%C A245326 If the rows are written in a right-aligned fashion:
%C A245326 1,
%C A245326 2,1,
%C A245326 3,3,2,1,
%C A245326 5,4,5,4,3,3,2,1,
%C A245326 8,7,7,5,8,7,7,5,5,4,5,4,3,3,2,1,
%C A245326 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,
%C A245326 then each column is constant and the terms are from A071585 (a(2^m-1-k) = A071585(k), k = 0,1,2,...).
%C A245326 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 the 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.
%H A245326 <a href="/index/Fo#fraction_trees">Index entries for fraction trees</a>
%F A245326 a(n) = A002487(1+A059893(A180200(n))) = A002487(A059893(A154435(n))). - _Yosu Yurramendi_, Sep 20 2021
%o A245326 (R)
%o A245326 blocklevel <- 6 # arbitrary
%o A245326 a <- 1
%o A245326 for(m in 0:blocklevel) for(k in 0:(2^(m-1)-1)){
%o A245326 a[2^(m+1)+k] <- a[2^m+k] + a[2^m+2^(m-1)+k]
%o A245326 a[2^(m+1)+2^(m-1)+k] <- a[2^(m+1)+k]
%o A245326 a[2^(m+1)+2^m+k] <- a[2^m+k]
%o A245326 a[2^(m+1)+2^m+2^(m-1)+k] <- a[2^m+2^(m-1)+k]
%o A245326 }
%o A245326 a
%o A245326 (PARI) a(n) = my(A=1); for(i=0, logint(n, 2), if(bittest(2*n, i), A++, A=(A+1)/A)); denominator(A) \\ _Mikhail Kurkov_, Feb 20 2023
%Y A245326 Cf. A245325, A002487, A071585, A071766, A273494.
%Y A245326 Cf. A002487, A059893, A154435.
%K A245326 nonn,frac
%O A245326 1,2
%A A245326 _Yosu Yurramendi_, Jul 18 2014