A199613 Decimal expansion of least x satisfying x^2+4*x*cos(x)=sin(x) (negated).

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

Offset: 1

Author

Clark Kimberling, Nov 08 2011

Keywords

• nonn
• cons

Comments

See A199597 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least: -1.077309917524072030339979615126813664791...
greatest: 3.553241680682892523957265556234494902067...
		

Links

• Iain Fox, Table of n, a(n) for n = 1..20000
• Index entries for transcendental numbers.

Crossrefs

Cf. A199597.

Programs

Mathematica

a = 1; b = 4; c = 1;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.1, -1.0}, WorkingPrecision -> 110]
RealDigits[r]  (* A199613, least of 4 roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3.5, 3.6}, WorkingPrecision -> 110]
RealDigits[r]  (* A199614, greatest of 4 roots *)

PARI

solve(x=-2, -1, x^2+4*x*cos(x)-sin(x)) \\ Iain Fox, Nov 22 2017