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A086751 Decimal expansion of the solution to x*sqrt(1-x^2) + arcsin(x) = Pi/4, or the length of the line connecting the origin to the center of the chord of a circle, centered at 0 and of radius 1, that divides the circle such that 1/4 of the area is on one side and 3/4 is on the other side. 0
4, 0, 3, 9, 7, 2, 7, 5, 3, 2, 9, 9, 5, 1, 7, 2, 0, 9, 3, 1, 8, 9, 6, 1, 7, 4, 0, 0, 6, 6, 3, 1, 5, 4, 4, 2, 9, 0, 2, 2, 3, 5, 9, 6, 4, 5, 7, 4, 0, 9, 8, 4, 2, 2, 2, 5, 0, 0, 9, 7, 6, 0, 1, 7, 3, 3, 8, 7, 0, 5, 4, 9, 9, 7, 1, 2, 9, 5, 3, 5, 3, 5, 0, 1, 2, 4, 3, 3, 9, 0, 1, 6, 5, 2, 2, 2, 7, 2, 8, 7, 0, 9, 4, 9, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..104.

FORMULA

Define k(n+1) to be k(n) - (k(n)sqrt(1-k(n)^2) + arcsin(k(n)) - Pi/4). The sequence is the decimal expansion of limit_{n -> infinity} k(n).

EXAMPLE

0.403972753299517...

MAPLE

Digits := 240 ; x := 0.4 ; for i from 1 to 8 do f := sin(2.0*x)+2.0*x-Pi/2.0 ; fp := 2*cos(2*x)+2.0 ; x := x-evalf(f/fp) ; printf("%.120f\n", sin(x)) ; od: x := sin(x) ; read("transforms3") ; CONSTTOLIST(x) ; # R. J. Mathar, May 19 2009

MATHEMATICA

digits = 105; Sin[FindRoot[Sin[2*a]/2+a == Pi/4, {a, 1/2}, WorkingPrecision -> digits][[1, 2]]] // RealDigits[#, 10, digits]& // First (* Jean-Fran├žois Alcover, Feb 21 2014 *)

CROSSREFS

Sequence in context: A246686 A048649 A200008 * A048281 A066273 A028650

Adjacent sequences:  A086748 A086749 A086750 * A086752 A086753 A086754

KEYWORD

cons,nonn,easy

AUTHOR

Jonathan R. Anderson (neo__jon(AT)hotmail.com), Jul 30 2003

EXTENSIONS

More terms from Jim Nastos, Sep 05 2003

More digits from R. J. Mathar, May 19 2009

STATUS

approved

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Last modified February 17 20:06 EST 2018. Contains 299296 sequences. (Running on oeis4.)