A201412 Decimal expansion of least x satisfying 5*x^2 = sec(x) and 0 < x < Pi.

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

Offset

0,1

Comments

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

Links

Table of n, a(n) for n=0..98.

Example

least:  0.474127690420775415934748938569551538434...
greatest: 1.4792710652904107931042853415537602633...

Mathematica

a = 5; 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, .4, .5}, WorkingPrecision -> 110]
RealDigits[r]     (* A201412 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r]    (* A201413 *)

Crossrefs

Cf. A201397.

Sequence in context: A365940 A365945 A365943 * A272056 A020803 A019626

Adjacent sequences: A201409 A201410 A201411 * A201413 A201414 A201415

Keyword

nonn,cons

Author

Clark Kimberling, Dec 01 2011

Status

approved