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A193506 Decimal expansion of bean curve perimeter. 1
3, 7, 5, 0, 2, 1, 3, 6, 4, 5, 1, 5, 7, 2, 4, 2, 5, 7, 1, 9, 2, 8, 2, 9, 5, 7, 9, 6, 6, 0, 5, 5, 1, 4, 0, 3, 1, 6, 1, 8, 2, 4, 5, 4, 8, 9, 8, 5, 1, 0, 4, 9, 1, 3, 0, 6, 0, 5, 0, 7, 8, 5, 9, 7, 8, 3, 9, 2, 0, 3, 0, 5, 9, 5, 5, 9, 8, 1, 4, 3, 1, 3, 0, 5, 7, 4, 2, 4, 8, 0, 2, 3, 2, 7, 9, 6, 2, 2, 6, 5, 1, 5, 9, 8, 6, 1, 8, 5, 7, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..110.

Eric Weisstein's World of Mathematics, Bean Curve

EXAMPLE

3.750213645...

MATHEMATICA

f[x_, y_] = x^4 + x^2*y^2 + y^4 - x*(x^2 + y^2); x1 = 1/3; x2 = 5/6; sx = Solve[f[x, y] == 0, x]; sy = Solve[f[x, y] == 0, y]; g1[y_] = x /. sx[[3]]; g2[y_] = x /. sx[[4]]; f[x_] = y /. sy[[4]]; p1 = NIntegrate[ Sqrt[1 + g1'[y]^2], {y, 0, f[x1]}, WorkingPrecision -> 120]; p2 = NIntegrate[ Sqrt[1 + f'[x]^2], {x, x1, x2}, WorkingPrecision -> 120]; p3 = NIntegrate[ Sqrt[1 + g2'[y]^2], {y, 0, f[x2]}, WorkingPrecision -> 120]; Take[ RealDigits[2*(p1+p2+p3)][[1]], 105]

Take[RealDigits[9/2 + NIntegrate[2 Sqrt[1 + (1 - 2 x + (1 + 3 x - 6 x^2)/Sqrt[1 + (2 - 3 x) x])^2/(8 x (1 - x + Sqrt[1 + (2 - 3 x) x]))] - 1/Sqrt[x] - 1/(2 (1 - x)^(3/4)) - 3/(8 (1 - x)^(1/4)), {x, 0, 1}, WorkingPrecision -> 220, PrecisionGoal -> 110, MaxRecursion -> 50]][[1]], 110] (* Eric W. Weisstein, Jul 23 2020 *)

CROSSREFS

Cf. A193505 (area).

Cf. A336501 (decimal expansion of the lima bean curve).

Sequence in context: A331733 A301755 A302558 * A086242 A322931 A096627

Adjacent sequences:  A193503 A193504 A193505 * A193507 A193508 A193509

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Jul 29 2011

STATUS

approved

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Last modified August 15 00:08 EDT 2022. Contains 356122 sequences. (Running on oeis4.)