The On-Line Encyclopedia of Integer Sequences (OEIS)

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A200299

Decimal expansion of least x satisfying 4*x^2 - 3*cos(x) = sin(x), negated.
(history; published version)

#9 by Alois P. Heinz at Mon Jul 09 19:48:42 EDT 2018

STATUS

reviewed

approved

#8 by Michel Marcus at Mon Jul 09 02:04:57 EDT 2018

STATUS

proposed

reviewed

#7 by G. C. Greubel at Sun Jul 08 21:51:55 EDT 2018

STATUS

editing

proposed

#6 by G. C. Greubel at Sun Jul 08 21:51:47 EDT 2018

NAME

Decimal expansion of least x satisfying 4*x^2 - 3*cos(x) = sin(x), negated.

LINKS

G. C. Greubel, <a href="/A200299/b200299.txt">Table of n, a(n) for n = 0..10000</a>

PROG

(PARI) a=4; b=-3; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jul 08 2018

STATUS

approved

editing

#5 by Russ Cox at Fri Mar 30 18:58:00 EDT 2012

AUTHOR

_Clark Kimberling (ck6(AT)evansville.edu), _, Nov 15 2011

Discussion

Fri Mar 30

18:58

OEIS Server: https://oeis.org/edit/global/285

#4 by T. D. Noe at Wed Nov 16 19:55:07 EST 2011

STATUS

proposed

approved

#3 by Clark Kimberling at Wed Nov 16 16:21:11 EST 2011

STATUS

editing

proposed

#2 by Clark Kimberling at Tue Nov 15 19:38:09 EST 2011

NAME

allocated for Clark KimberlingDecimal expansion of least x satisfying 4*x^2-3*cos(x)=sin(x).

DATA

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

OFFSET

0,1

COMMENTS

See A199949 for a guide to related sequences. The Mathematica program includes a graph.

EXAMPLE

least x: -0.661826141188850993743026123357094...

greatest x: 0.8308503276605474027666209935665...

MATHEMATICA

a = 4; b = -3; c = 1;

f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]

Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]

r = x /. FindRoot[f[x] == g[x], {x, -.67, -.66}, WorkingPrecision -> 110]

RealDigits[r] (* A200299 *)

r = x /. FindRoot[f[x] == g[x], {x, .83, .84}, WorkingPrecision -> 110]

RealDigits[r] (* A200300 *)

CROSSREFS

Cf. A199949.

KEYWORD

allocated

nonn,cons

AUTHOR

Clark Kimberling (ck6(AT)evansville.edu), Nov 15 2011

STATUS

approved

editing

#1 by Clark Kimberling at Tue Nov 15 15:01:35 EST 2011

NAME

allocated for Clark Kimberling

KEYWORD

allocated

STATUS

approved