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 A161638 #22 Mar 17 2025 22:14:02 %S A161638 1,1,2,2,1,1,2,3,2,2,1,1,2,2,3,3,2,2,4,3,1,1,2,2,3,3,2,2,3,2,1,1,2,3, %T A161638 3,2,3,4,4,3,2,2,4,3,1,1,2,2,2,4,2,3,5,3,3,3,2,2,4,4,3,3,1,1,2,3,2,3, %U A161638 4,3,2,2,3,3,4,3,2,2,1,1,2,3,2,3,3,3,2 %N A161638 The largest number of steps in Euclid's algorithm applied to A157807(n) and A157813(n). %C A161638 The sequence of fractions is ordered as follows: 1/1, 2/1, 1/2, 1/3, 3/1, 4/1, 3/2, 2/3, 1/4, 1/5, 5/1,... %H A161638 Anonymous, <a href="http://eom.springer.de/E/e036320.htm">Euclidean algorithm</a>, Springer's Encyclopedia of Maths. %H A161638 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/EuclideanAlgorithm.html">Euclidean algorithm</a>, MathWorld. %H A161638 Wikipedia, <a href="http://en.wikipedia.org/wiki/Euclid's_algorithm">Euclid's algorithm</a> %e A161638 a(8) = 3 because the algorithm applied to the pair (2,3) needs the steps 2 = 3 x 0 + 2 then 3 = 2 x 1 + 1 and 2 = 1 x 2 + 0. %o A161638 (Python) %o A161638 from math import gcd %o A161638 def euclid_steps(a, b): %o A161638 if b == 0: %o A161638 return 0 %o A161638 else: %o A161638 return 1 + euclid_steps(b, a % b) %o A161638 for s in range(2, 100, 2): %o A161638 for i in range(1, s): %o A161638 if gcd(i, s - i) != 1: continue %o A161638 print(euclid_steps(i, s - i)) %o A161638 for i in range(s, 0, -1): %o A161638 if gcd(i, s + 1 - i) != 1: continue %o A161638 print(euclid_steps(i, s + 1 - i)) %o A161638 # _Hiroaki Yamanouchi_, Oct 06 2014 %K A161638 nonn,easy %O A161638 1,3 %A A161638 _Yalcin Aktar_, Jun 15 2009 %E A161638 Partially edited by _R. J. Mathar_, Sep 23 2009 %E A161638 a(1) prepended and a(12)-a(87) added by _Hiroaki Yamanouchi_, Oct 06 2014