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A199613 Decimal expansion of least x satisfying x^2+4*x*cos(x)=sin(x) (negated). 3
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

Iain Fox, Table of n, a(n) for n = 1..20000

EXAMPLE

least: -1.077309917524072030339979615126813664791...

greatest: 3.553241680682892523957265556234494902067...

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 *)

PROG

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

CROSSREFS

Cf. A199597.

Sequence in context: A318302 A266271 A021568 * A136141 A264806 A197843

Adjacent sequences:  A199610 A199611 A199612 * A199614 A199615 A199616

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Nov 08 2011

STATUS

approved

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Last modified February 28 01:46 EST 2020. Contains 332319 sequences. (Running on oeis4.)