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 A374987 #5 Oct 02 2024 14:28:38
%S A374987 6,14,24,32,40,48,58,66,74,82,92,100,108,116,126,134,142,150,160,168,
%T A374987 176,184,194,202,210,218,228,236,244,254,262,270,278,288,296,304,312,
%U A374987 322,330,338,346,356,364,372,382,390,398,406,416,424,432,440,450,458
%N A374987 Let s(x) be the Maclaurin series for cos(x); then a(n) is the least index k for which all partial sums of cos(2m*Pi) are positive.
%e A374987 For n=1, the partial sums (for k = 0,1,2,3,4,5,6,7) are approximately 1, -18.7, 46.2, -39.2, 20.9, -5.4, 2.4, 0.7; beginning with k=6, the partials sums are all positive, so a(1)=6.
%t A374987 z = 800; r = Pi;
%t A374987 f[m_, n_] := f[m, n] = N[Sum[(-1)^k (2 m r)^(2 k)/(2 k)!, {k, 0, n}], 10]
%t A374987 g[m_] := Select[Range[z], f[m, #] > 0 && f[m, # + 1] > 0 &, 1]
%t A374987 Flatten[Table[g[m], {m, 1, 80}]]
%Y A374987 Cf. A376456, A376457, A375057, A375053, A375054.
%K A374987 nonn
%O A374987 0,1
%A A374987 _Clark Kimberling_, Oct 01 2024