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.

6, 14, 24, 32, 40, 48, 58, 66, 74, 82, 92, 100, 108, 116, 126, 134, 142, 150, 160, 168, 176, 184, 194, 202, 210, 218, 228, 236, 244, 254, 262, 270, 278, 288, 296, 304, 312, 322, 330, 338, 346, 356, 364, 372, 382, 390, 398, 406, 416, 424, 432, 440, 450, 458

Offset

0,1

Links

Table of n, a(n) for n=0..53.

Example

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.

Mathematica

z = 800; r = Pi;
f[m_, n_] := f[m, n] = N[Sum[(-1)^k  (2 m  r)^(2 k)/(2 k)!, {k, 0, n}], 10]
g[m_] := Select[Range[z], f[m, #] > 0 && f[m, # + 1] > 0 &, 1]
Flatten[Table[g[m], {m, 1, 80}]]

Crossrefs

Cf. A376456, A376457, A375057, A375053, A375054.

Sequence in context: A005281 A120345 A107400 * A104675 A028557 A083657

Adjacent sequences: A374984 A374985 A374986 * A374988 A374989 A374990

Keyword

nonn

Author

Clark Kimberling, Oct 01 2024

Status

approved