A201674 Decimal expansion of least x satisfying 7*x^2 - 1 = csc(x) and 0

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

Offset: 0

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:  0.62272709431369510379503993928652289013...
greatest:  3.12676335481784395832471054304139350...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Index entries for transcendental numbers.

Crossrefs

Cf. A201564.

Programs

Mathematica

a = 7; c = -1;
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, .6, .7}, WorkingPrecision -> 110]
RealDigits[r]     (* A201674 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.14}, WorkingPrecision -> 110]
RealDigits[r]     (* A201675 *)

PARI

a=7; c=-1; solve(x=0.5, 1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Sep 12 2018