A206291 - OEIS

A206291

Decimal expansion of the middle zero x(2) of the function F(x) = f(f(x)) - x, where f(x) = cos(x) - sin(x).

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

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OFFSET

0,1

COMMENTS

The decimal expansions of the other two zeros (x(1) and x(3)) of F(x) are A216891 and A216863, respectively. See the Comments at A216891 for more information on the properties of these zeros.

LINKS

Table of n, a(n) for n=0..104.

Roman Wituła, Damian Słota and Szeged Problem Group 'Fejéntaláltuka', An Iteration Convergence: 11318[2007,745], Amer. Math. Monthly, Vol. 116, No. 7 (2009), 648-649.

EXAMPLE

We have f(x(2)) = x(2) = 0.45662470456763..., sin(x(2)) = 0.4409211... and x(2) - sin(x(2)) > 0.015703...

MATHEMATICA

f[x_] := Cos[x] - Sin[x]; F[x_] := f[f[x]] - x; RealDigits[x /. FindRoot[F[x], {x, 0}, WorkingPrecision -> 120]][[1]] (* Amiram Eldar, Mar 27 2026 *)

CROSSREFS

Cf. A216891, A216863, A215668, A215670, A215832, A215833, A168546.

Sequence in context: A134299 A112780 A021223 * A058979 A225491 A046343

Adjacent sequences: A206288 A206289 A206290 * A206292 A206293 A206294

KEYWORD

nonn,cons

AUTHOR

Roman Witula, Sep 22 2012

STATUS

approved