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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.
7
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
1,1
FORMULA
|a(n)-A376457(n)| = 1 for n>=1.
EXAMPLE
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.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Oct 01 2024
STATUS
approved