A199049 Decimal expansion of x > 0 satisfying x^2 + sin(x) = 3.

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

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: -1.979320146556211460335749713988...
positive:  1.4183100916225250456919496008037...

Mathematica

a = 1; b = 1; c = 3;
f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -3, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.98, -1.97}, WorkingPrecision -> 110]
RealDigits[r] (* A199048 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r] (* A199049 *)

Prog

(PARI) a=1; b=1; c=3; solve(x=0, 1.5, a*x^2 - c + b*sin(x)) \\ G. C. Greubel, Feb 19 2019
(Sage) a=1; b=1; c=3; (a*x^2 + b*sin(x)==c).find_root(0, 2, x) # G. C. Greubel, Feb 19 2019

Crossrefs

Cf. A198866, A199048.

Sequence in context: A130297 A271478 A112032 * A145917 A201661 A263498

Adjacent sequences: A199046 A199047 A199048 * A199050 A199051 A199052

Keyword

nonn,cons

Author

Clark Kimberling, Nov 02 2011

Status

approved