The On-Line Encyclopedia of Integer Sequences (OEIS)

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A199605

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

#5 by Russ Cox at Fri Mar 30 18:57:58 EDT 2012

AUTHOR

_Clark Kimberling (ck6(AT)evansville.edu), _, Nov 08 2011

Discussion

Fri Mar 30

18:57

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

#4 by T. D. Noe at Tue Nov 08 18:18:57 EST 2011

STATUS

proposed

approved

#3 by Clark Kimberling at Tue Nov 08 17:19:06 EST 2011

STATUS

editing

proposed

#2 by Clark Kimberling at Tue Nov 08 15:35:56 EST 2011

NAME

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

DATA

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

OFFSET

0,1

COMMENTS

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

EXAMPLE

least: -0.93049500263597010976334102402547851258644...

greatest: 3.01796308106862887266781443388576897037832...

MATHEMATICA

a = 1; b = 3; c = 1;

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

Plot[{f[x], g[x]}, {x, -1.5, 3.5}, {AxesOrigin -> {0, 0}}]

r = x /. FindRoot[f[x] == g[x], {x, -1, -.9}, WorkingPrecision -> 110]

RealDigits[r] (* A199605, least of 4 roots *)

r = x /. FindRoot[f[x] == g[x], {x, 3, 3.1}, WorkingPrecision -> 110]

RealDigits[r] (* A199606, greatest of 4 roots *)

CROSSREFS

Cf. A199597.

KEYWORD

allocated

nonn,cons

AUTHOR

Clark Kimberling (ck6(AT)evansville.edu), Nov 08 2011

STATUS

approved

editing

#1 by Clark Kimberling at Tue Nov 08 13:40:30 EST 2011

NAME

allocated for Clark Kimberling

KEYWORD

allocated

STATUS

approved