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A201572 Decimal expansion of least x satisfying x^2 + 6 = csc(x) and 0 < x < Pi. 3
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 (list; constant; graph; refs; listen; history; text; internal format)
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

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Last modified July 25 02:57 EDT 2021. Contains 346282 sequences. (Running on oeis4.)