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A204619 Decimal expansion of arc length of the Keratoid Cusp curve (loop arc length). 0
5, 1, 0, 0, 9, 4, 9, 4, 1, 8, 0, 3, 4, 7, 0, 2, 7, 4, 2, 5, 0, 7, 3, 2, 6, 2, 3, 7, 3, 3, 5, 3, 4, 8, 8, 2, 9, 0, 5, 3, 5, 4, 6, 9, 8, 3, 0, 5, 2, 5, 1, 4, 7, 9, 0, 8, 8, 6, 0, 4, 2, 4, 4, 6, 1, 0, 8, 7, 3, 1, 9, 1, 3, 7, 4, 7, 8, 8, 1, 7, 4, 5, 4, 3, 1, 2, 9, 5, 4, 2, 2, 1, 9, 8, 0, 1, 4, 1, 5, 2, 1, 6, 7, 2, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..104.

Eric Weisstein's World of Mathematics, Keratoid Cusp

EXAMPLE

0.5100949418...

MATHEMATICA

eq = y^2 == x^2*y + x^5; f1[x_] = y /. Solve[eq, y][[1]]; f2[x_] = y /. Solve[eq, y][[2]]; x1 = (x - 1/4)/2 /. Solve[f2'[x] == 0][[1]]; y1 = f1[x1]; y2 = f2[x1]; g[y_] = x /. Solve[eq, x][[1]]; gp[y_] := (2*y - g[y]^2)/(2*y*g[y] + 5*g[y]^4); ni[a_, b_] := NIntegrate[a, b, WorkingPrecision -> 120]; i1 = ni[Sqrt[1 + f1'[x]^2], {x, x1, 0}]; i2 = ni[Sqrt[1 + f2'[x]^2], {x, x1, 0}]; i3 = ni[Sqrt[1 + gp[y]^2], {y, y1, y2}]; Take[RealDigits[i1 + i2 + i3][[1]], 105] (* Jean-François Alcover, Jan 17 2012 *)

CROSSREFS

Sequence in context: A269129 A320606 A058177 * A228077 A204170 A283784

Adjacent sequences:  A204616 A204617 A204618 * A204620 A204621 A204622

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, Jan 17 2012

EXTENSIONS

Offset corrected by Rick L. Shepherd, Jan 05 2014

STATUS

approved

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Last modified October 23 23:51 EDT 2019. Contains 328379 sequences. (Running on oeis4.)