The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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-François Alcover, Aug 03 2011 *) CROSSREFS Sequence in context: A246184 A197478 A260713 * A350362 A351120 A199664 Adjacent sequences:  A101798 A101799 A101800 * A101802 A101803 A101804 KEYWORD nonn,cons AUTHOR Eric W. Weisstein, Dec 16 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 25 09:45 EDT 2022. Contains 354066 sequences. (Running on oeis4.)