A199046 Decimal expansion of x<0 satisfying x^2 + sin(x) = 2.

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

Offset

1,2

Comments

See A198866 for a guide to related sequences. The Mathematica program includes a graph.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Example

negative: -1.72846631899717722235659184827479...
positive:  1.06154977463138382560203340351989...

Mathematica

a = 1; b = 1; c = 2;
f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.73, -1.72}, WorkingPrecision -> 110]
RealDigits[r] (* A199046 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.06, 1.07}, WorkingPrecision -> 110]
RealDigits[r] (* A199047 *)

Prog

(PARI) a=1; b=1; c=0; solve(x=-2, 0, a*x^2 - c + b*sin(x)) \\ G. C. Greubel, Feb 19 2019
(Sage) a=1; b=1; c=2; (a*x^2 + b*sin(x)==c).find_root(-2, 0, x) # G. C. Greubel, Feb 19 2019

Crossrefs

Cf. A198866.

Sequence in context: A201322 A093753 A249506 * A198564 A259072 A107311

Adjacent sequences: A199043 A199044 A199045 * A199047 A199048 A199049

Keyword

nonn,cons

Author

Clark Kimberling, Nov 02 2011

Status

approved