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A201516 Decimal expansion of greatest x satisfying 3*x^2 - 1 = sec(x) and 0 < x < Pi. 3
1, 3, 4, 1, 4, 3, 0, 1, 6, 6, 2, 9, 1, 2, 5, 9, 7, 6, 4, 5, 7, 6, 0, 8, 0, 5, 0, 6, 7, 6, 3, 6, 1, 4, 1, 7, 1, 7, 7, 1, 4, 0, 8, 2, 9, 1, 7, 9, 4, 8, 3, 0, 1, 1, 3, 0, 7, 5, 1, 6, 4, 3, 7, 7, 1, 8, 0, 4, 9, 8, 8, 2, 4, 9, 6, 7, 8, 0, 0, 0, 6, 9, 8, 5, 4, 2, 0, 4, 6, 3, 0, 5, 8, 6, 0, 2, 4, 9, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A201397 for a guide to related sequences. The Mathematica program includes a graph.

LINKS

Table of n, a(n) for n=1..99.

EXAMPLE

least:  0.95353909754991468966727069537237822743...

greatest: 1.341430166291259764576080506763614171...

MATHEMATICA

a = 3; c = -1;

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

Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]

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

RealDigits[r]   (* A201515 *)

r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.5}, WorkingPrecision -> 110]

RealDigits[r]  (* A201516 *)

CROSSREFS

Cf. A201397.

Sequence in context: A131129 A087694 A010262 * A105579 A124446 A293190

Adjacent sequences:  A201513 A201514 A201515 * A201517 A201518 A201519

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Dec 02 2011

STATUS

approved

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Last modified May 12 11:55 EDT 2021. Contains 343821 sequences. (Running on oeis4.)