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A201519
Decimal expansion of least x satisfying 5*x^2 - 1 = sec(x) and 0 < x < Pi.
3
6, 7, 5, 4, 8, 2, 9, 0, 8, 1, 1, 3, 7, 2, 4, 2, 2, 8, 0, 1, 5, 1, 7, 8, 8, 5, 8, 1, 9, 0, 8, 2, 7, 3, 1, 5, 9, 4, 1, 0, 7, 4, 0, 1, 2, 5, 4, 4, 0, 8, 8, 0, 7, 9, 6, 4, 4, 8, 5, 0, 8, 0, 4, 5, 2, 7, 2, 3, 7, 1, 5, 8, 0, 3, 2, 5, 1, 7, 3, 9, 1, 3, 5, 7, 5, 5, 1, 1, 7, 5, 3, 3, 0, 3, 5, 5, 2, 1, 1
OFFSET
0,1
COMMENTS
See A201397 for a guide to related sequences. The Mathematica program includes a graph.
EXAMPLE
least: 0.675482908113724228015178858190...
greatest: 1.4683742920332829376554687815...
MATHEMATICA
a = 5; 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, .6, .7}, WorkingPrecision -> 110]
RealDigits[r] (* A201519 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r] (* A201520 *)
CROSSREFS
Cf. A201397.
Sequence in context: A100124 A355336 A190648 * A198507 A021152 A199720
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 02 2011
STATUS
approved