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 A238837 #29 Aug 19 2020 02:57:34 %S A238837 0,1,1,2,3,1,2,3,5,4,5,1,2,3,3,4,7,7,8,5,7,7,8,1,2,3,3,4,5,4,5,5,9,10, %T A238837 11,9,12,11,13,6,9,10,11,9,12,11,13,1,2,3,3,4,5,4,5,5,7,7,8,5,7,7,8,6, %U A238837 11,13,14,13,17,15,18,11,16,17,19,14,19,18,21 %N A238837 Numerators in the enumeration of the rationals by Czyz and Self. %C A238837 Denominators are A071766(n) for n >= 1. %C A238837 Differs from A229742 by 1 at the integer rational positions n = 2^k because Czyz and Self only increment the last continued fraction term when there are two or more terms. So a(n) = A229742(n) - A209229(n) for n >= 1. %H A238837 Rémy Sigrist, <a href="/A238837/b238837.txt">Table of n, a(n) for n = 1..10000</a> %H A238837 Jerzy Czyz and William Self, <a href="http://www.jstor.org/stable/3595818">The Rationals Are Countable: Euclid's Proof</a>, The College Mathematics Journal, volume 34, number 5, November 2003, pages 367-369. %o A238837 (PARI) a(n) = my (w=[]); while (n, my (v=valuation(n,2)); w=concat(w, 1+v); n \= 2^(v+1)); w[#w]--; my (r=w[1] + (#w>1)); for (k=2, #w, r=w[k]+1/r); numerator(r) \\ _Rémy Sigrist_, Aug 25 2018 %Y A238837 Cf. A071766, A209229, A229742. %K A238837 nonn,frac,look %O A238837 1,4 %A A238837 _N. J. A. Sloane_, Mar 14 2014, following a suggestion from _Kevin Ryde_ %E A238837 More terms from _Rémy Sigrist_, Aug 25 2018