A075838 Decimal expansion of the solution to the donkey problem.

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

Offset

0,1

Links

Table of n, a(n) for n=0..95.

Dr. Math, Grazing Animals.

Marshall Fraser, A tale of two goats, Math. Mag., 55 (1982), 221-227. [N. J. A. Sloane, Jul 12 2011]

Formula

x: 4x*cos^2(x) + (1/2)Pi - 2x - sin(2x) = 0.

Example

0.95284786465494194744133321858048335174752156080640...

Mathematica

RealDigits[x /. FindRoot[4*x*Cos[x]^2 + Pi/2 - 2*x - Sin[2*x] == 0, {x, 1}, WorkingPrecision -> 120], 10, 105][[1]] (* Amiram Eldar, Apr 29 2023 *)

Prog

(PARI) solve(x=0, 1, 4*x*cos(x)^2 + Pi/2 - 2*x - sin(2*x)) \\ Michel Marcus, Sep 19 2017

Crossrefs

Cf. A133731, A173571, A192930.

Sequence in context: A155165 A199061 A346573 * A094129 A021917 A128757

Adjacent sequences: A075835 A075836 A075837 * A075839 A075840 A075841

Keyword

easy,nonn,cons

Author

Zak Seidov, Oct 17 2002

Status

approved