A199083 Decimal expansion of x>0 satisfying x^2 + 2*sin(x) = 2.

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

Offset: 0

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: -1.96188424641083489341928077977489...
positive:  0.774980814423043445958593502470401...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Index entries for transcendental numbers.

Crossrefs

Cf. A198866, A199082.

Programs

Mathematica

a = 1; b = 2; 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, -1.97, -1.96}, WorkingPrecision -> 110]
RealDigits[r](* A199082 *)
r = x/.FindRoot[f[x] == g[x], {x, .77, .78}, WorkingPrecision -> 110]
RealDigits[r](* This sequence *)

PARI

a=1; b=2; c=2; solve(x=0, 1, a*x^2 + b*sin(x) - c) \\ G. C. Greubel, Feb 20 2019

Sage

a=1; b=2; c=2; (a*x^2 + b*sin(x)==c).find_root(0,1,x) # G. C. Greubel, Feb 20 2019

Extensions

Terms a(90) onward corrected by G. C. Greubel, Feb 20 2019