A199293 Decimal expansion of x < 0 satisfying 3*x^2 + 3*x*cos(x) = 2.

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

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..101.

Example

negative: -1.0835116610219289883304749103821255...
positive:  0.48645750461686637457544128449375285...

Mathematica

a = 3; b = 3; c = 2;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1, -.9}, WorkingPrecision -> 110]
RealDigits[r]    (* A199293 *)
r = x /. FindRoot[f[x] == g[x], {x, .48, .49}, WorkingPrecision -> 110]
RealDigits[r]    (* A199294 *)

Crossrefs

Cf. A199170, A199294.

Sequence in context: A202779 A328498 A199440 * A357108 A110234 A334073

Adjacent sequences: A199290 A199291 A199292 * A199294 A199295 A199296

Keyword

nonn,cons

Author

Clark Kimberling, Nov 05 2011

Extensions

a(90) onwards corrected by Georg Fischer, Aug 03 2021

Status

approved