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

Author

Zak Seidov, Oct 17 2002

Keywords

• easy
• nonn
• cons

Examples

			0.95284786465494194744133321858048335174752156080640...
		

Links

• Dr. Math, Grazing Animals.
• Marshall Fraser, A tale of two goats, Math. Mag., 55 (1982), 221-227. [_N. J. A. Sloane_, Jul 12 2011]

Crossrefs

Cf. A133731, A173571, A192930.

Programs

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 *)

PARI

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

Formula

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