

A193626


Decimal expansion of bicuspid curve length.


1



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

1,1


LINKS

Table of n, a(n) for n=1..105.
Eric Weisstein's World of Mathematics, BicuspidCurve.


EXAMPLE

9.861772942...


MATHEMATICA

f[x_, y_] = (x^2  1)*(x  1)^2 + (y^2  1)^2; sy = Solve[f[x, y] == 0, y]; sx = Solve[f[x, y] == 0, x]; s = Solve[f[x, x + 1/2] == 0, x] ; f1[x_] = y /. sy[[4, 1]]; f2[x_] = y /. sy[[2, 1]]; g1[y_] = x /. sx[[3, 1]]; g2[y_] = x /. sx[[4, 1]]; x2 = x /. s[[3]]; y2 = f1[x2]; x6 = x /. s[[4]]; y6 = f2[x6]; ni[a_, b_] := NIntegrate[a, b, WorkingPrecision > 120]; ds1 = Sqrt[1 + f1'[x]^2] // Simplify; p1 = ni[ds1, {x, x2, 1} ] ; ds2 = Sqrt[1 + g1'[y]^2]; p2 = ni[ds2, {y, 0, y2}] ; ds3 = Sqrt[1 + g2'[y]^2]; p3 = ni[ds3, {y, 0, y6}] ; ds4 = Sqrt[1 + f2'[x]^2] // Simplify; p4 = ni[ds4, {x, x6, 1}] ; p = 2*(p1 + p2 + p3 + p4) ; Take[RealDigits[p][[1]], 105]


CROSSREFS

Cf. A193625 (area)
Sequence in context: A059069 A084660 A002391 * A316600 A087044 A246168
Adjacent sequences: A193623 A193624 A193625 * A193627 A193628 A193629


KEYWORD

nonn,cons


AUTHOR

JeanFrançois Alcover, Aug 01 2011


STATUS

approved



