

A332331


Decimal expansion of the nexttoleast positive zero of the 12th Maclaurin polynomial of cos x.


0



4, 6, 8, 6, 5, 1, 7, 6, 6, 3, 7, 9, 5, 7, 5, 7, 4, 4, 6, 5, 7, 0, 0, 4, 8, 9, 8, 3, 7, 9, 0, 7, 7, 5, 0, 6, 6, 8, 2, 7, 1, 2, 2, 0, 1, 7, 5, 9, 6, 6, 4, 5, 8, 3, 2, 3, 1, 0, 5, 8, 7, 1, 3, 7, 5, 3, 7, 1, 4, 0, 7, 8, 7, 6, 1, 6, 8, 6, 8, 2, 0, 3, 9, 2, 5, 1
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OFFSET

1,1


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 nexttoleast positive zero of p(2n,x) if there is such a zero. The limit of z(n) is 3 Pi/2 = 4.7123889..., as in A197723.


LINKS

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


EXAMPLE

Nexttoleast positive zero = 4.6865176637957574465700489837907750...


MATHEMATICA

z = 150; p[n_, x_] := Normal[Series[Cos[x], {x, 0, n}]]
t = x /. NSolve[p[12, x] == 0, x, z][[8]]
u = RealDigits[t][[1]]
Plot[Evaluate[p[12, x]], {x, 1, 5}]


CROSSREFS

Cf. A197723, A332329, A332330.
Sequence in context: A201336 A244850 A188930 * A159576 A199626 A163639
Adjacent sequences: A332328 A332329 A332330 * A332332 A332333 A332334


KEYWORD

nonn,cons,easy


AUTHOR

Clark Kimberling, Feb 11 2020


STATUS

approved



