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 A362602 #31 Apr 30 2023 18:17:37
%S A362602 6,19,44,333,710,103993,312689,2292816,4272943,10838702,80143857,
%T A362602 411557987,2549491779,14885392687,42106686282,1783366216531,
%U A362602 8958937768937,288469374822515,856449186698608,5706674932067741,12269799050834090,30246273033735921,133254891185777774
%N A362602 Integers in the interval [Pi*k - 1/k, Pi*k + 1/k] for some k > 0 that are numerators of convergents to 2*Pi.
%C A362602 Conjecture: the sequence is infinite.
%t A362602 hmax=30; A046955=Join[{1}, Numerator[Convergents[2Pi, hmax]]]; a={}; For[h=2, h<=hmax, h++, k=Intersection[List[Floor[Last[x/.N[Solve[Pi*x^2 - 1 - Part[A046955,h] x == 0, x], 2*hmax]]]], List[Ceiling[Last[x/.N[Solve[Pi*x^2 + 1 - Part[A046955,h] x == 0, x], 2*hmax]]]]]; If[k!={} && Ceiling[k*Pi - 1/k] == Floor[k*Pi + 1/k], AppendTo[a,Part[A046955,h]]]]; a
%Y A362602 Intersection of A046955 and A265735.
%K A362602 nonn
%O A362602 1,1
%A A362602 _Alexander R. Povolotsky_ and _Stefano Spezia_, Apr 27 2023