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 A071647 #23 Apr 19 2025 03:59:54
%S A071647 1,1,2,2,3,2,3,4,3,3,4,4,5,4,4,4,4,5,5,4,6,4,5,4,5,5,5,5,6,6,6,5,5,7,
%T A071647 5,5,6,5,6,6,6,6,6,6,6,6,7,6,7,7,6,6,6,5,8,6,6,6,6,7,6,6,6,7,7,7,7,7,
%U A071647 7,6,7,6,7,7,7,8,6,6,8,8,8,7,7,6,7,7,7
%N A071647 a(n) is the maximum number of elements among the continued fractions for n/1, n/2, n/3, n/4, ..., n/n.
%C A071647 a(n)/log(n) is bounded.
%C A071647 Apart from initial term, same as A034883. - _Franklin T. Adams-Watters_, Nov 14 2006
%H A071647 Jinyuan Wang, <a href="/A071647/b071647.txt">Table of n, a(n) for n = 1..1000</a>
%e A071647 Continued fractions for 5/1 = [5]; 5/2 = [2, 2]; 5/3 = [1, 1, 2]; 5/4 = [1, 4]; 5/5 = [1]. Hence a(5) = 3.
%t A071647 a[n_] := Max[Table[Length[ContinuedFraction[n/k]], {k, 1, n}]]; Array[a, 100] (* _Amiram Eldar_, Apr 19 2025 *)
%o A071647 (PARI) for(n=1,150,print1( vecmax(vector(n,i,length(contfrac(n/i)))),","))
%Y A071647 Cf. A034883, A071677.
%K A071647 nonn,easy
%O A071647 1,3
%A A071647 _Benoit Cloitre_, Jun 22 2002