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A193751 Decimal expansion of Pear curve length. 1
7, 7, 3, 8, 3, 7, 3, 6, 2, 4, 1, 3, 3, 4, 9, 8, 3, 6, 1, 9, 9, 9, 8, 4, 4, 4, 1, 0, 7, 0, 4, 4, 8, 6, 1, 4, 0, 2, 3, 4, 8, 7, 4, 9, 5, 1, 7, 9, 4, 3, 8, 8, 5, 5, 8, 9, 3, 8, 4, 0, 0, 0, 4, 8, 3, 1, 5, 0, 7, 9, 4, 1, 7, 2, 5, 2, 2, 3, 3, 6, 1, 7, 5, 1, 7, 8, 6, 6, 4, 4, 8, 0, 5, 7, 4, 5, 8, 8, 1, 1, 8, 9, 7, 2, 9 (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

7.738373624...

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]]; sg = Solve[f[g[y], y] == 0 && D[f[g[y], y], y] == 0 , g'[y]][[1]]; dg1[y_] = g'[y] /. sg /. g -> g1;

dg2[y_] = g'[y] /. sg /. g -> g2; ni[a_, b_] := NIntegrate[a, b, WorkingPrecision -> 120];

i1 = ni[Sqrt[1 + dg1[y]^2], {y, 0, f2[-1]} ];

i2 = ni[Sqrt[1 + f2'[x]^2], {x, -1, x2}];

i3 = ni[Sqrt[1 + dg2[y]^2], {y, 0, y2}];

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

CROSSREFS

Cf. A193750 (area)

Sequence in context: A155959 A063736 A212299 * A290565 A319263 A318386

Adjacent sequences:  A193748 A193749 A193750 * A193752 A193753 A193754

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, Aug 03 2011

EXTENSIONS

Corrected and extended by Jean-François Alcover, Aug 26 2011

STATUS

approved

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Last modified December 16 09:06 EST 2019. Contains 330020 sequences. (Running on oeis4.)