A201572 Decimal expansion of least x satisfying x^2 + 6 = csc(x) and 0 < x < Pi.

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

Offset

0,2

Comments

See A201564 for a guide to related sequences. The Mathematica program includes a graph.

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Example

least:  0.166669163175400949565200320627761299158167...
greatest:  3.076894929246192023166693647327725773248...

Mathematica

a = 1; c = 6;
f[x_] := a*x^2 + c; g[x_] := Csc[x]
Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .1, .2}, WorkingPrecision -> 110]
RealDigits[r]   (* A201572 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
RealDigits[r]   (* A201573 *)

Prog

(PARI) a=1; c=6; solve(x=0.1, .2, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 21 2018

Crossrefs

Cf. A201564.

Sequence in context: A243758 A318355 A318237 * A261468 A001734 A342373

Adjacent sequences: A201569 A201570 A201571 * A201573 A201574 A201575

Keyword

nonn,cons

Author

Clark Kimberling, Dec 03 2011

Extensions

Terms a(83) onward corrected by G. C. Greubel, Aug 21 2018

Status

approved