A199047 Decimal expansion of x>0 satisfying x^2 + sin(x) = 2.

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

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

Links

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

Crossrefs

Cf. A198866.

Programs

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 *)

PARI

a=1; b=1; c=2; solve(x=0, 1.5, 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(0,2,x) # G. C. Greubel, Feb 19 2019

Extensions

Terms a(87) onward corrected by G. C. Greubel, Feb 19 2019