A199081 Decimal expansion of x > 0 satisfying x^2 + 2*sin(x) = 1.

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

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: -1.7251712054289301271344240020632...
positive:  0.42302818188516042885129332473260...
		

Links

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

Crossrefs

Cf. A198866, A199080.

Programs

Mathematica

a = 1; b = 2; c = 1;
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, -1.8, -1.7}, WorkingPrecision -> 110]
RealDigits[r]   (* A199080 *)
r = x /. FindRoot[f[x] == g[x], {x, .42, .43}, WorkingPrecision -> 110]
RealDigits[r]   (* A199081 *)

PARI

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

Sage

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

Extensions

Terms a(83) onward corrected by G. C. Greubel, Feb 20 2019