A198867 Decimal expansion of x > 0 satisfying x^2 + sin(x) = 1.

6, 3, 6, 7, 3, 2, 6, 5, 0, 8, 0, 5, 2, 8, 2, 0, 1, 0, 8, 8, 7, 9, 9, 0, 9, 0, 3, 8, 3, 8, 2, 8, 0, 0, 5, 8, 9, 9, 7, 8, 0, 5, 0, 7, 8, 8, 4, 1, 7, 9, 1, 6, 7, 3, 3, 8, 2, 8, 1, 8, 2, 6, 3, 1, 9, 5, 8, 0, 4, 4, 0, 2, 9, 0, 1, 2, 0, 2, 5, 9, 2, 6, 5, 1, 4, 5, 9, 4, 7, 3, 1, 1, 8, 0, 7, 4, 5, 9, 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: -1.40962400400259624923559397058949354...
positive:  0.63673265080528201088799090383828005...
		

Links

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

Crossrefs

Cf. A198866.

Programs

Mathematica

a = 1; b = 1; 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, -1.41, -1.40}, WorkingPrecision -> 110]
RealDigits[r] (* A198866 *)
r = x /. FindRoot[f[x] == g[x], {x, .63, .64}, WorkingPrecision -> 110]
RealDigits[r] (* A198867 *)

PARI

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

Sage

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