A376456 Let s(x) be the Maclaurin series for cos(x); then a(n) is the index k for which the (k+1)-st partial sum of s(2*n*Pi) is greatest among all partial sums.

2, 6, 8, 12, 14, 18, 22, 24, 28, 30, 34, 36, 40, 44, 46, 50, 52, 56, 58, 62, 66, 68, 72, 74, 78, 80, 84, 88, 90, 94, 96, 100, 102, 106, 110, 112, 116, 118, 122, 124, 128, 132, 134, 138, 140, 144, 146, 150, 154, 156, 160, 162, 166, 168, 172, 176, 178, 182

Offset: 1

Author

Clark Kimberling, Sep 26 2024

Keywords

• nonn

Examples

			For n = 2 the partial sums (of which the 1st is for k=0) are approximately 1, -18.7, 46.2, -39.2, 20.9, -5.4,..., where the greatest, 46.2..., is the 3rd, so that a(2) = 2.
		

Crossrefs

Cf. A376457.

Programs

Mathematica

z = 200; r = Pi;
f[n_, m_] := f[n, m] = N[Sum[(-1)^k  (2 n  r)^(2 k)/(2 k)!, {k, 0, m}], 10]
t[n_] := Table[f[n, m], {m, 1, z}]
g[n_] := Select[Range[z], f[n, #] == Max[t[n]] &]
h[n_] := Select[Range[z], f[n, #] == Min[t[n]] &]
Flatten[Table[g[n], {n, 1, 60}]]  (* this sequence *)
Flatten[Table[h[n], {n, 1, 60}]]  (* A376457 *)

Formula

|a(n)-A376457(n)| = 1 for n>=1.