A201422 Decimal expansion of least x satisfying 10*x^2 = sec(x) and 0 < x < Pi.

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

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:  0.3248357625526726343272168905918357...
greatest: 1.52794989469861441964924475246801...

Mathematica

a = 10; 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]    (* A201422 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
RealDigits[r]    (* A201423 *)

Crossrefs

Cf. A201397.

Sequence in context: A229976 A084695 A317704 * A231330 A254051 A082228

Adjacent sequences: A201419 A201420 A201421 * A201423 A201424 A201425

Keyword

nonn,cons

Author

Clark Kimberling, Dec 02 2011

Status

approved