A193781 Decimal expansion of the perimeter of the second Mandelbrot set lemniscate.

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

Offset

1,1

Links

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

Eric Weisstein's World of Mathematics, Mandelbrot Set Lemniscate

Example

8.8944968157...

Mathematica

f[x_, y_] = (x^2 + y^2)*((x + 1)^2 + y^2) - 4; f[x_] = y /. Solve[f[x, y] == 0, y][[4]]; g[y_] = x /. Solve[f[x, y] == 0, x][[4]]; Take[RealDigits[ 4*NIntegrate[Sqrt[1 + f'[x]^2], {x, -1/2, 0}, WorkingPrecision -> 120] + 4*NIntegrate[Sqrt[1 + g'[y]^2], {y, 0, f[0]}, WorkingPrecision -> 120]][[1]], 105]

Crossrefs

Cf. A193780 (area).

Sequence in context: A346908 A195717 A309930 * A200492 A154707 A121309

Adjacent sequences: A193778 A193779 A193780 * A193782 A193783 A193784

Keyword

nonn,cons

Author

Jean-François Alcover, Aug 05 2011

Status

approved