A376457 Let s(x) be the Maclaurin series for cos(x); then a(n) is the index k for which (k+1)-st partial sum of s(2*n*Pi) is least among all partial sums.

3, 5, 9, 11, 15, 19, 21, 25, 27, 31, 33, 37, 41, 43, 47, 49, 53, 55, 59, 63, 65, 69, 71, 75, 77, 81, 85, 87, 91, 93, 97, 99, 103, 107, 109, 113, 115, 119, 121, 125, 129, 131, 135, 137, 141, 143, 147, 151, 153, 157, 159, 163, 165, 169, 173, 175, 179, 181, 185

Offset: 1

Author

Clark Kimberling, Oct 01 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 least, -39.2..., is the 4th, so that a(2) = 3.
		

Crossrefs

Cf. A374987, A375057, A375053, A375054.

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}]]  (* A376456 *)
Flatten[Table[h[n], {n, 1, 60}]]  (* this sequence *)

Formula

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