

A118811


Decimal expansion of arc length of the (first) butterfly curve.


0



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

1,1


LINKS

Table of n, a(n) for n=1..99.
Eric Weisstein's World of Mathematics, Butterfly Curve


EXAMPLE

9.0173569856546976918...


MATHEMATICA

eq = y^6 == x^2x^6; f[x_] = y /. Solve[eq, y][[2]]; g[y_] = x /. Solve[eq, x][[2]]; h[y_] = x /. Solve[eq, x][[4]]; x1 = 3/8; y1 = f[x1]; x2 = 7/8; y2 = f[x2]; ni[a_, b_] := NIntegrate[a, b, WorkingPrecision > 120]; i1 = ni[Sqrt[1+f'[x]^2], {x, x1, x2}]; i2 = ni[Sqrt[1+g'[y]^2], {y, 0, y2}]; i3 = ni[Sqrt[1+h'[y]^2], {y, 0, y1}]; Take[RealDigits[4(i1+i2+i3)][[1]], 99](* JeanFrançois Alcover, Jan 19 2012 *)


PROG

(PARI) 4*intnum(x=0, 1, sqrt(1+(x/3x^5)^2/(x^2x^6)^(5/3))) \\ Charles R Greathouse IV, Jan 17 2012


CROSSREFS

Cf. A118292.
Sequence in context: A226120 A244593 A277524 * A200488 A249418 A256036
Adjacent sequences: A118808 A118809 A118810 * A118812 A118813 A118814


KEYWORD

nonn,cons


AUTHOR

Eric W. Weisstein, Apr 30 2006


EXTENSIONS

Last digit corrected by Eric W. Weisstein, Jan 18 2012


STATUS

approved



