A343487 Decimal expansion of the perimeter of the convex hull around the terdragon fractal.

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

Offset

1,1

Comments

The convex hull around the terdragon fractal has 14 sides and with unit length from curve start to end their lengths are four sqrt(3)/24 and two each 1/24, 1/8, sqrt(3)/8, 3/8, sqrt(37)/12. Their total is the perimeter.

Links

Kevin Ryde, Table of n, a(n) for n = 1..10000

Kevin Ryde, Iterations of the Terdragon Curve, see index "HBf".

Formula

Equals (13 + 5*sqrt(3) + 2*sqrt(37)) / 12.

Equals (13 + sqrt(223 + 20*sqrt(3*37))) / 12.

Largest root of ((12*x - 13)^2 - 223)^2 - 44400 = 0 (all its roots are real).

Example

2.8188149248700688204697166831611246...

Mathematica

RealDigits[(13+5*Sqrt[3]+2*Sqrt[37])/12, 10, 120][[1]] (* Harvey P. Dale, Dec 25 2021 *)

Prog

(PARI) my(c=223+20*quadgen(3*37*4)); a_vector(len) = my(s=10^(len-1)); digits((13*s + sqrtint(floor(c*s^2))) \12);

Crossrefs

Cf. A343486 (terdragon hull area), A341030 (dragon hull perimeter).

Sequence in context: A254277 A244688 A086037 * A199787 A165274 A221074

Adjacent sequences: A343484 A343485 A343486 * A343488 A343489 A343490

Keyword

cons,easy,nonn

Author

Kevin Ryde, Apr 17 2021

Status

approved