A199609 Decimal expansion of least x>0 satisfying x^2+3*x*cos(x)=3*sin(x).

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

Offset

1,3

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: 1.14225640224474011004461587823586435251534483...
greatest:  3.0656207603368585618674575528508213250654...

Mathematica

a = 1; b = 3; c = 3;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]
RealDigits[r]  (* A199609, least x>0 of 3 roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3, 3.1}, WorkingPrecision -> 110]
RealDigits[r]  (* A199610, greatest of 3 roots *)

Crossrefs

Cf. A199597.

Sequence in context: A334232 A244681 A023634 * A284692 A019834 A261557

Adjacent sequences: A199606 A199607 A199608 * A199610 A199611 A199612

Keyword

nonn,cons

Author

Clark Kimberling, Nov 08 2011

Status

approved