A199183 Decimal expansion of greatest x satisfying x^2 + 3*x*cos(x) = 1.

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

Offset: 1

Author

Clark Kimberling, Nov 04 2011

Keywords

• nonn
• cons

Comments

See A199170 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least: -1.3606727725137972152286027487379925...
greatest: 3.27746466341373058734587727791083...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A199170, A199182.

Programs

Mathematica

a = 1; b = 3; c = 1;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -2 Pi, 2 Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.4, -1.3}, WorkingPrecision -> 110]
RealDigits[r]   (* A199182  least of four roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3.27, 3.28}, WorkingPrecision -> 110]
RealDigits[r]   (* A199183  greatest of four roots *)

Extensions

a(92) onwards corrected by Georg Fischer, Aug 03 2021