The On-Line Encyclopedia of Integer Sequences (OEIS)

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A198356

Decimal expansion of greatest x having 4*x^2+x=4*cos(x).
(history; published version)

#6 by Charles R Greathouse IV at Fri Feb 07 16:44:05 EST 2025

COMMENTS

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

Discussion

Fri Feb 07

16:44

OEIS Server: https://oeis.org/edit/global/3013

#5 by Russ Cox at Fri Mar 30 18:57:54 EDT 2012

AUTHOR

_Clark Kimberling (ck6(AT)evansville.edu), _, Oct 24 2011

Discussion

Fri Mar 30

18:57

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

#4 by T. D. Noe at Mon Oct 24 21:19:06 EDT 2011

STATUS

proposed

approved

#3 by Clark Kimberling at Mon Oct 24 20:23:51 EDT 2011

STATUS

editing

proposed

#2 by Clark Kimberling at Mon Oct 24 10:27:05 EDT 2011

NAME

allocated for Clark KimberlingDecimal expansion of greatest x having 4*x^2+x=4*cos(x).

DATA

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

OFFSET

0,1

COMMENTS

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

EXAMPLE

least x: -0.91555432657358705292706966750136951...

greatest x: 0.7424374889656033785172455301643263...

MATHEMATICA

a = 4; b = 1; c = 4;

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

Plot[{f[x], g[x]}, {x, -1, 1}]

r1 = x /. FindRoot[f[x] == g[x], {x, -1, -.9}, WorkingPrecision -> 110]

RealDigits[r1] (* A198355 *)

r2 = x /. FindRoot[f[x] == g[x], {x, .74, .75}, WorkingPrecision -> 110]

RealDigits[r2] (* A198356 *)

CROSSREFS

Cf. A197737.

KEYWORD

allocated

nonn,cons

AUTHOR

Clark Kimberling (ck6(AT)evansville.edu), Oct 24 2011

STATUS

approved

editing

#1 by Clark Kimberling at Sun Oct 23 15:14:25 EDT 2011

NAME

allocated for Clark Kimberling

KEYWORD

allocated

STATUS

approved