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A201417 Decimal expansion of greatest x satisfying 7*x^2 = sec(x) and 0 < x < Pi. 3
1, 5, 0, 7, 9, 2, 8, 7, 9, 5, 3, 8, 0, 0, 9, 8, 2, 6, 6, 5, 6, 7, 8, 9, 9, 9, 9, 4, 0, 7, 0, 9, 9, 1, 4, 1, 3, 3, 9, 9, 6, 3, 0, 1, 1, 4, 6, 2, 2, 2, 1, 0, 4, 1, 8, 0, 3, 0, 5, 4, 5, 7, 3, 5, 2, 6, 3, 9, 4, 0, 3, 2, 6, 3, 3, 9, 6, 3, 2, 6, 5, 4, 9, 7, 2, 1, 7, 5, 5, 1, 3, 4, 9, 7, 3, 7, 6, 4, 3 (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:  0.39327382732884150383245205720625342659...

greatest: 1.507928795380098266567899994070991413...

MATHEMATICA

a = 7; c = 0;

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, .3, .4}, WorkingPrecision -> 110]

RealDigits[r]    (* A201416 *)

r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]

RealDigits[r]    (* A201417 *)

CROSSREFS

Cf. A201397.

Sequence in context: A155827 A244045 A084248 * A147666 A343071 A215892

Adjacent sequences:  A201414 A201415 A201416 * A201418 A201419 A201420

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Dec 01 2011

STATUS

approved

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Last modified January 29 02:10 EST 2022. Contains 350672 sequences. (Running on oeis4.)