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A193750 Decimal expansion of Pear curve area 1
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 (list; constant; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Aug 03 2011

STATUS

approved

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Last modified April 23 05:34 EDT 2021. Contains 343199 sequences. (Running on oeis4.)