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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.

A376953 a(n) = least k such that (n*Pi/3)^(2k)/(2 k)! < 1.

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%I A376953 #8 Oct 16 2024 21:37:36
%S A376953 1,1,2,4,5,6,8,9,11,12,13,15,16,18,19,20,22,23,25,26,27,29,30,32,33,
%T A376953 35,36,37,39,40,42,43,44,46,47,49,50,52,53,54,56,57,59,60,61,63,64,66,
%U A376953 67,69,70,71,73,74,76,77,78,80,81,83,84,86,87,88,90,91,93
%N A376953 a(n) = least k such that (n*Pi/3)^(2k)/(2 k)! < 1.
%C A376953 The numbers (n*Pi/3)^(2k)/(2 k)! are the coefficients in the Maclaurin series for cos x when x = n*Pi/3.  If m>a(n), then (m*Pi/3)^(2k)/(2 k)! < 1. A375057 is a trisection of this sequence.
%F A376953 a(n) ~ Pi*exp(1)*n/6 - log(n)/4. - _Vaclav Kotesovec_, Oct 13 2024
%t A376953 a[n_] := Select[Range[300], (n Pi/3)^(2 #)/(2 #)! < 1 &, 1];
%t A376953 Flatten[Table[a[n], {n, 0, 200}]]
%Y A376953 Cf. A370507, A376952, A376954, A376955, A376956, A376957, A376958, A376959, A376960.
%K A376953 nonn
%O A376953 0,3
%A A376953 _Clark Kimberling_, Oct 12 2024