

A201590


Decimal expansion of greatest x satisfying 5*x^2 = csc(x) and 0 < x < Pi.


3



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

1,1


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 = 1..10000


EXAMPLE

least: 0.596626819860704546761832859082141048303653100...
greatest: 3.121059463523827415360175700034092048910749...


MATHEMATICA

a = 5; 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] (* A201589 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision > 110]
RealDigits[r] (* A201590 *)


PROG

(PARI) a=5; c=0; solve(x=3.1, 3.14, a*x^2 + c  1/sin(x)) \\ G. C. Greubel, Aug 22 2018


CROSSREFS

Cf. A201564.
Sequence in context: A255615 A056931 A139569 * A235358 A086249 A176784
Adjacent sequences: A201587 A201588 A201589 * A201591 A201592 A201593


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Dec 03 2011


EXTENSIONS

Terms a(88) onward corrected by G. C. Greubel, Aug 22 2018


STATUS

approved



