A199612 Decimal expansion of greatest x satisfying x + 4*cos(x) = 0.

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

Offset

1,1

Comments

See A199597 for a guide to related sequences. The Mathematica program includes a graph.

Links

Table of n, a(n) for n=1..99.

Example

least: -1.25235323400258876318632812197538043590128...
greatest:  3.595304867161547991877606935083418714913111...

Mathematica

a = 1; b = 4; c = 0;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.3, -1.2}, WorkingPrecision -> 110]
RealDigits[r]  (* A199611, least of 4 roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3.5, 3.6}, WorkingPrecision -> 110]
RealDigits[r]  (* A199612, greatest of 4 roots *)

Crossrefs

Cf. A199597, A199611.

Sequence in context: A189044 A299793 A356527 * A076844 A198558 A286566

Adjacent sequences: A199609 A199610 A199611 * A199613 A199614 A199615

Keyword

nonn,cons

Author

Clark Kimberling, Nov 08 2011

Extensions

a(86) onwards corrected by Georg Fischer, Aug 03 2021

Status

approved