A201738 Decimal expansion of greatest x satisfying x^2 - 4 = csc(x) and 0

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

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.

There is a greatest number c for which x^2-c=csc(x) for some number x satisfying 0

Examples

			least:  2.31504693361737481767157626271919435080...
greatest:  2.91834369901820138765983699207605876...
		

Links

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

Crossrefs

Cf. A201564.

Programs

Mathematica

a = 1; c = -4;
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, 2.3, 2.4}, WorkingPrecision -> 110]
RealDigits[r]   (* A201737 *)
r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]
RealDigits[r]   (* A201738 *)

PARI

a=1; c=-4; solve(x=2.5, 3, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Sep 12 2018

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