login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; constant; graph; refs; listen; history; text; internal format)
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

Jean-Fran├žois Alcover, Aug 01 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 20 02:22 EDT 2019. Contains 323411 sequences. (Running on oeis4.)