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 A046965 #17 Feb 16 2020 14:35:32
%S A046965 1,2,3,22,355,104348,208341,521030,833719,1146408,5419351,85563208,
%T A046965 165707065,245850922,657408909,1068966896,3618458675,6167950454,
%U A046965 21053343141,1804419559672,3587785776203,5371151992734,14330089761671,130796280757852
%N A046965 Cos(a(n)) decreases monotonically to -1.
%C A046965 May be computed found using convergents to the continued fraction for Pi. If cos(a(n)) is near -1, then a(n) is near an odd multiple of Pi. That is, a(n)/(2k+1) is a good rational approximation to Pi with an odd denominator (and continued fractions give good rational approximations).
%C A046965 If a convergent of the continued fraction for Pi has an odd denominator then the corresponding numerator is a term in this sequence. Otherwise add one to the last term in the convergent to get an approximation of Pi with an odd denominator. In this case, we may get a duplicate of the next convergent which we may just ignore.
%C A046965 To illustrate: [3] = 3/1 -> 3; [3,7] = 22/7 -> 22; [3,7,15] = 333/106; 106 is even -> [3,7,16] = 355/113 -> 355; [3,7,15,1] = 355/113 -> 355 (ignore); [3,7,15,1,292] = 103993/33102 -> [3,7,15,1,293] = 104348/33215 -> 104348
%t A046965 z={}; current=1; Timing[ Do[ If[ Cos[ n ]<current, AppendTo[ z, current=Cos[ n ] ] ], {n, 105000} ] ]; z
%Y A046965 Cf. A001203 for the continued fraction for Pi.
%K A046965 nonn
%O A046965 1,2
%A A046965 _Wouter Meeussen_
%E A046965 More terms from _Michel ten Voorde_
%E A046965 Terms a(13) and beyond and comments from Jonathan Cross (jcross(AT)wcox.com), Oct 16 2001
%E A046965 Offset changed to 1 by _Alois P. Heinz_, Apr 12 2019