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A332327 Decimal expansion of the least positive zero of the 6th Maclaurin polynomial of cos x. 1
1, 5, 6, 9, 9, 0, 5, 8, 2, 5, 1, 6, 1, 1, 9, 1, 4, 5, 6, 6, 1, 8, 1, 2, 2, 1, 8, 5, 7, 8, 1, 8, 2, 9, 7, 4, 8, 3, 7, 2, 4, 5, 2, 3, 2, 5, 4, 9, 7, 3, 1, 6, 8, 3, 7, 1, 2, 4, 8, 9, 5, 4, 6, 9, 2, 0, 0, 6, 3, 4, 4, 5, 3, 2, 4, 4, 6, 5, 2, 7, 2, 8, 2, 5, 6, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The Maclaurin polynomial p(2n,x) of cos x is 1 - x^2/2! + x^4/4! + ... + (-1)^n x^(2n)/(2n)!.

Let z(n) be the least positive zero of p(2n,x).  The limit of z(n) is Pi/2 = 1.570796326..., as in A019669.

LINKS

Table of n, a(n) for n=1..86.

EXAMPLE

Least positive zero = 1.56990582516119145661812218578182974...

MATHEMATICA

z = 150; p[n_, x_] := Normal[Series[Cos[x], {x, 0, n}]]

t = x /. NSolve[p[6, x] == 0, x, z][[4]]

u = RealDigits[t][[1]]

Plot[Evaluate[p[6, x]], {x, -1, 2}]

CROSSREFS

Cf. A019669, A332326.

Sequence in context: A118261 A246749 A021641 * A260635 A306016 A087176

Adjacent sequences:  A332324 A332325 A332326 * A332328 A332329 A332330

KEYWORD

nonn,cons,easy

AUTHOR

Clark Kimberling, Feb 11 2020

STATUS

approved

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Last modified October 17 02:45 EDT 2021. Contains 348048 sequences. (Running on oeis4.)