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 A293248 #9 Oct 05 2017 09:54:32 %S A293248 1,1,2,1,3,1,2,3,4,1,5,1,2,5,6,1,3,5,7,1,2,4,5,7,8,1,3,7,9,1,2,3,4,7, %T A293248 8,9,10,1,5,7,11,1,2,5,6,7,8,11,12,1,3,5,3,4,9,11,13,1,2,4,11,13,14,1, %U A293248 3,5,11,13,15,1,2,3,4,5,6,11,12,13,14,15,16 %N A293248 Let S be the sequence of rational numbers generated by these rules: 1 is in S, and if u/v is in S (with gcd(u, v) = 1), then (u+1)/v and u/(v+1) are in S, and duplicates are deleted as they occur; a(n) = the denominator of the n-th term of S. %C A293248 See A293247 for the corresponding numerators, and additional comments. %H A293248 Rémy Sigrist, <a href="/A293248/b293248.txt">Table of n, a(n) for n = 1..10000</a> %H A293248 Rémy Sigrist, <a href="/A293248/a293248.gp.txt">PARI program for A293248</a> %e A293248 S(1) = 1 by definition; so a(1) = 1. %e A293248 (1+1)/1 = 2 has not yet occurred; so S(2) = 2 and a(2) = 1. %e A293248 1/(1+1) = 1/2 has not yet occurred; so S(3) = 1/2 and a(3) = 2. %e A293248 (2+1)/1 = 3 has not yet occurred; so S(4) = 3 and a(4) = 1. %e A293248 2/(1+1) = 1 has already occurred. %o A293248 (PARI) See Links section. %Y A293248 Cf. A293247. %K A293248 nonn,frac %O A293248 1,3 %A A293248 _Rémy Sigrist_, Oct 03 2017