A199268 Decimal expansion of x > 0 satisfying 2*x^2 + x*cos(x) = 3.

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

Offset

1,3

Comments

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

Links

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

Example

negative: -1.29477176551027054190068103147021856144266...
positive:  1.120827899072464105010802655123824414841540...

Mathematica

a = 2; b = 1; c = 3;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.3, -1.2}, WorkingPrecision -> 110]
RealDigits[r]    (* A199267 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.12, 1.13}, WorkingPrecision -> 110]
RealDigits[r]    (* A199268 *)

Crossrefs

Cf. A199170, A199267.

Sequence in context: A305809 A349139 A159810 * A268499 A298522 A206436

Adjacent sequences: A199265 A199266 A199267 * A199269 A199270 A199271

Keyword

nonn,cons

Author

Clark Kimberling, Nov 04 2011

Extensions

a(89) onwards corrected by Georg Fischer, Aug 03 2021

Status

approved