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A193781
Decimal expansion of the perimeter of the second Mandelbrot set lemniscate.
1
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
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
KEYWORD
nonn,cons
AUTHOR
STATUS
approved