The On-Line Encyclopedia of Integer Sequences (OEIS)

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A197812

Decimal expansion of x>0 having x^2+x=3*cos(x).
(history; published version)

#5 by Russ Cox at Fri Mar 30 18:57:53 EDT 2012

AUTHOR

_Clark Kimberling (ck6(AT)evansville.edu), _, Oct 20 2011

Discussion

Fri Mar 30

18:57

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

#4 by T. D. Noe at Thu Oct 20 20:37:34 EDT 2011

STATUS

proposed

approved

#3 by Clark Kimberling at Thu Oct 20 20:20:42 EDT 2011

STATUS

editing

proposed

#2 by Clark Kimberling at Thu Oct 20 19:36:22 EDT 2011

NAME

allocated for Clark KimberlingDecimal expansion of x>0 having x^2+x=3*cos(x).

DATA

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

OFFSET

0,1

COMMENTS

See A197737 for a guide to related sequences. The Mathematica program includes a graph.

EXAMPLE

negative: -1.389437452704828389291498251429189255963...

positive: 0.9297344303618125096887004946976108824038...

MATHEMATICA

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

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

Plot[{f[x], g[x]}, {x, -2, 1.5}]

r1 = x /. FindRoot[f[x] == g[x], {x, -1.4, -1.3}, WorkingPrecision -> 110]

RealDigits[r1] (* A197811 *)

r2 = x /. FindRoot[f[x] == g[x], {x, .92, .93}, WorkingPrecision -> 110]

RealDigits[r2] (* A197812 *)

CROSSREFS

Cf. A197737.

KEYWORD

allocated

nonn,cons

AUTHOR

Clark Kimberling (ck6(AT)evansville.edu), Oct 20 2011

STATUS

approved

editing

#1 by Clark Kimberling at Tue Oct 18 11:25:01 EDT 2011

NAME

allocated for Clark Kimberling

KEYWORD

allocated

STATUS

approved