A199179 Decimal expansion of x > 0 satisfying x^2 + 2*x*cos(x) = 2.

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

Offset

0,1

Comments

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

Links

Table of n, a(n) for n=0..98.

Example

negative: -1.493519280868891056556339509934781825...
positive:  0.94494832910354696494592764037834555...

Mathematica

a = 1; b = 2; c = 2;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -5, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.5, -1.4}, WorkingPrecision -> 110]
RealDigits[r]  (* A199178 *)
r = x /. FindRoot[f[x] == g[x], {x, .2, .53}, WorkingPrecision -> 110]
RealDigits[r]   (* A199179 *)

Crossrefs

Cf. A199170, A199178.

Sequence in context: A340578 A378486 A374225 * A344949 A300072 A062546

Adjacent sequences: A199176 A199177 A199178 * A199180 A199181 A199182

Keyword

nonn,cons

Author

Clark Kimberling, Nov 04 2011

Extensions

a(95) onwards corrected by Georg Fischer, Aug 03 2021

Status

approved