A193750 - OEIS

%I #25 Dec 10 2018 09:31:17

%S 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,

%T 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,

%U 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

%N Decimal expansion of Pear curve area

%C The Pear Curve is the third Mandelbrot set lemniscate.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PearCurve.html">Pear Curve</a>

%e 4.1465267894...

%t 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}];

%t Take[RealDigits[2(i1 + i2 + i3)][[1]], 105]

%Y Cf. A193751 (length).

%K nonn,cons

%O 1,1

%A _Jean-François Alcover_, Aug 03 2011