A201657 Decimal expansion of greatest x satisfying 8*x^2 = csc(x) and 0 < x < Pi.

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

Offset: 1

Author

Clark Kimberling, Dec 04 2011

Keywords

• nonn
• cons

Comments

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

Examples

			least:  0.507262199349103778265812147726404197638586...
greatest:  3.128823571901654937275752484725028832935...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Index entries for transcendental numbers.

Crossrefs

Cf. A201564.

Programs

Mathematica

a = 8; c = 0;
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, .5, .6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201656 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
RealDigits[r]   (* A201657 *)

PARI

a=8; c=0; solve(x=3, 3.14, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 23 2018