The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A201656

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A201656

Decimal expansion of least x satisfying 8*x^2 = csc(x) and 0 < x < Pi.
(history; published version)

#10 by Susanna Cuyler at Thu Aug 23 02:14:11 EDT 2018

STATUS

proposed

approved

#9 by Jon E. Schoenfield at Wed Aug 22 23:50:02 EDT 2018

STATUS

editing

proposed

#8 by Jon E. Schoenfield at Wed Aug 22 23:49:59 EDT 2018

NAME

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

STATUS

proposed

editing

#7 by G. C. Greubel at Wed Aug 22 23:34:46 EDT 2018

STATUS

editing

proposed

#6 by G. C. Greubel at Wed Aug 22 23:34:41 EDT 2018

NAME

Decimal expansion of least x satisfying 8*x^2 = csc(x) and 0<x<piPi.

LINKS

G. C. Greubel, <a href="/A201656/b201656.txt">Table of n, a(n) for n = 0..10000</a>

PROG

(PARI) a=8; c=0; solve(x=0.5, 1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 22 2018

STATUS

approved

editing

#5 by Russ Cox at Fri Mar 30 18:58:02 EDT 2012

AUTHOR

_Clark Kimberling (ck6(AT)evansville.edu), _, Dec 04 2011

Discussion

Fri Mar 30

18:58

OEIS Server: https://oeis.org/edit/global/285

#4 by T. D. Noe at Sun Dec 04 18:42:21 EST 2011

STATUS

proposed

approved

#3 by Clark Kimberling at Sun Dec 04 16:40:42 EST 2011

STATUS

editing

proposed

#2 by Clark Kimberling at Sun Dec 04 10:04:49 EST 2011

NAME

allocated for Clark KimberlingDecimal expansion of least x satisfying 8*x^2=csc(x) and 0<x<pi.

DATA

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

OFFSET

0,1

COMMENTS

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

EXAMPLE

least: 0.507262199349103778265812147726404197638586...

greatest: 3.128823571901654937275752484725028832935...

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 *)

CROSSREFS

Cf. A201564.

KEYWORD

allocated

nonn,cons

AUTHOR

Clark Kimberling (ck6(AT)evansville.edu), Dec 04 2011

STATUS

approved

editing

#1 by Clark Kimberling at Sat Dec 03 17:16:56 EST 2011

NAME

allocated for Clark Kimberling

KEYWORD

allocated

STATUS

approved