A193750 Decimal expansion of Pear curve area

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

Offset

1,1

Comments

The Pear Curve is the third Mandelbrot set lemniscate.

Links

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

Eric Weisstein's World of Mathematics, Pear Curve

Example

4.1465267894...

Mathematica

f[x_, y_] = ComplexExpand[#*Conjugate[#] &[c + (c + c^2)^2] /. c -> x + I*y] - 4; sy = Solve[f[x, y] == 0, y]; f2[x_] = y /. sy[[4]]; x2 = 3/10; y2 = f2[x2]; sx = Solve[f[x, y] == 0, x]; g1[y_] = x /. sx[[1]]; g2[y_] = x /. sx[[2]]; ni[a_, b_] := NIntegrate[a, b, WorkingPrecision -> 120]; i1 = ni[-g1[y] - 1, {y, 0, f2[-1]} ]; i2 = ni[f2[x], {x, -1, x2}]; i3 = ni[g2[y] - x2, {y, 0, y2}];
Take[RealDigits[2(i1 + i2 + i3)][[1]], 105]

Crossrefs

Cf. A193751 (length).

Sequence in context: A205848 A297701 A110361 * A092856 A051006 A072812

Adjacent sequences: A193747 A193748 A193749 * A193751 A193752 A193753

Keyword

nonn,cons

Author

Jean-François Alcover, Aug 03 2011

Status

approved