A199048 Decimal expansion of x < 0 satisfying x^2 + sin(x) = 3.

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

Offset: 1

Author

Clark Kimberling, Nov 02 2011

Keywords

• nonn
• cons

Comments

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

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Index entries for transcendental numbers.

Crossrefs

Cf. A198866, A199049.

Programs

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] (* this sequence *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r] (* A199049 *)

PARI

a=1; b=1; c=3; solve(x=-2, 0, 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(-2,0,x) # G. C. Greubel, Feb 19 2019