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A101801 Decimal expansion of the area of the ampersand curve. 1
1, 0, 6, 6, 5, 5, 5, 0, 9, 5, 4, 5, 7, 3, 2, 7, 4, 6, 3, 7, 5, 3, 9, 1, 3, 9, 1, 3, 3, 6, 9, 1, 1, 9, 1, 3, 5, 7, 5, 5, 3, 9, 2, 3, 3, 9, 8, 4, 7, 7, 4, 9, 8, 9, 0, 2, 3, 7, 1, 7, 7, 0, 4, 4, 6, 4, 0, 4, 9, 8, 9, 3, 5, 1, 5, 1, 7, 9, 3, 2, 4, 8, 3, 8, 1, 1, 8, 0, 2, 1, 8, 7, 7, 1, 9, 9, 7, 2, 5, 7, 3, 0, 6, 6, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..105.

Eric Weisstein's World of Mathematics, Ampersand Curve

EXAMPLE

1.06655509...

MATHEMATICA

eq = (y^2 - x^2)(x - 1)(2x - 3) == 4 (x^2 + y^2 - 2x)^2 ;

sy = Solve[eq, y]; f1[x_] = y /. sy[[2]]; f2[x_] = y /. sy[[4]]; x1 = x /.    FindRoot[f1'[x] == 1, {x, 31/21}, WorkingPrecision -> 120 ]; y1 = y /. Solve[eq /. x -> x1][[3]]; y2 =  y /. Solve[eq /. x -> x1][[4]]; sx = Solve[eq, x]; g1[y_] = x /. sx[[1]]; g2[y_] = Simplify[x /. sx[[4]], y1 < y < y2]; ni[a_, b_] := NIntegrate[a, b, WorkingPrecision -> 120]; i1 = ni[Simplify[-g1[y], 0 < y < Sqrt[3]/2] , {y, 0, Sqrt[3]/2}]; i2 = ni[f2[x] - f1[x], {x, 0, 1}]; i3 = ni[f2[x] - f1[x], {x, 1, x1}]; i4 = ni[g2[y] - x1 , {y, y1, y2}]; Take[RealDigits[2 (i1 + i2 + i3 + i4)][[1]], 105]

(* Jean-Fran├žois Alcover, Aug 03 2011 *)

CROSSREFS

Sequence in context: A246184 A197478 A260713 * A199664 A019180 A019103

Adjacent sequences:  A101798 A101799 A101800 * A101802 A101803 A101804

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein, Dec 16 2004

STATUS

approved

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Last modified July 15 20:24 EDT 2019. Contains 325056 sequences. (Running on oeis4.)