A199614 Decimal expansion of greatest x satisfying x^2+4*x*cos(x)=sin(x).

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

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..99.

Example

least: -1.077309917524072030339979615126813664791...
greatest:  3.553241680682892523957265556234494902...

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 *)

Crossrefs

Cf. A199597.

Sequence in context: A320477 A110551 A141334 * A129488 A211023 A279494

Adjacent sequences: A199611 A199612 A199613 * A199615 A199616 A199617

Keyword

nonn,cons

Author

Clark Kimberling, Nov 08 2011

Status

approved