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A201528
Decimal expansion of greatest x satisfying 9*x^2 - 1 = sec(x) and 0 < x < Pi.
3
1, 5, 2, 0, 2, 7, 2, 4, 7, 6, 5, 0, 6, 1, 5, 0, 3, 4, 5, 9, 5, 9, 8, 4, 3, 5, 7, 6, 7, 9, 4, 3, 8, 3, 0, 6, 3, 0, 4, 2, 1, 6, 3, 8, 0, 6, 1, 0, 2, 5, 7, 5, 3, 9, 3, 3, 2, 7, 0, 7, 3, 2, 6, 4, 6, 0, 7, 6, 8, 0, 7, 7, 6, 2, 1, 2, 1, 3, 7, 2, 4, 4, 6, 1, 0, 5, 4, 5, 3, 5, 0, 0, 9, 2, 6, 7, 1, 0, 0
OFFSET
1,2
COMMENTS
See A201397 for a guide to related sequences. The Mathematica program includes a graph.
EXAMPLE
least: 0.4866365134428287964150106888774053061...
greatest: 1.52027247650615034595984357679438306...
MATHEMATICA
a = 9; 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, .4, .5}, WorkingPrecision -> 110]
RealDigits[r] (* A201527 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
RealDigits[r] (* A201528 *)
CROSSREFS
Cf. A201397.
Sequence in context: A244813 A078110 A334708 * A093814 A212155 A269328
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 02 2011
STATUS
approved