The On-Line Encyclopedia of Integer Sequences (OEIS)

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A198120

Decimal expansion of least x having 2*x^2-3x=-cos(x).
(history; published version)

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

AUTHOR

_Clark Kimberling (ck6(AT)evansville.edu), _, Oct 21 2011

Discussion

Fri Mar 30

18:57

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

#5 by T. D. Noe at Sun Oct 23 13:26:03 EDT 2011

STATUS

proposed

approved

#4 by Clark Kimberling at Sat Oct 22 15:31:34 EDT 2011

STATUS

editing

proposed

#3 by Clark Kimberling at Fri Oct 21 17:48:54 EDT 2011

NAME

Decimal expansion of least x having 2*x^2-3x=-cos(x).

EXAMPLE

least x: 0.42341886743695639025490191456713742341886743695639025490191456713...

greatest x: 1.463362827296431145105296426161346336282729643114510529642616...

#2 by Clark Kimberling at Fri Oct 21 17:44:26 EDT 2011

NAME

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

DATA

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

OFFSET

0,1

COMMENTS

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

EXAMPLE

least x: 0.423418867436956390254901914567137...

greatest x: 1.4633628272964311451052964261613...

MATHEMATICA

a = 2; b = -3; c = -1;

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

Plot[{f[x], g[x]}, {x, -1, 2}]

r1 = x /. FindRoot[f[x] == g[x], {x, -.43, -.42}, WorkingPrecision -> 110]

RealDigits[r1](* A198120 *)

r2 = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]

RealDigits[r2](* A198121 *)

CROSSREFS

Cf. A197737.

KEYWORD

allocated

nonn,cons

AUTHOR

Clark Kimberling (ck6(AT)evansville.edu), Oct 21 2011

STATUS

approved

editing

#1 by Clark Kimberling at Fri Oct 21 11:17:15 EDT 2011

NAME

allocated for Clark Kimberling

KEYWORD

allocated

STATUS

approved