A349010 Decimal expansion of the perimeter of the convex hull around the R5 dragon fractal.

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

Offset

1,1

Comments

The fractal is taken scaled to unit length from curve start to end.

With complex b = 1+2i, the hull sides are a countably infinite set: +-(4-i)/b^2, +-2/b^2, and 2*i^d/b^k for d=0..3 and k>=3. The sum of their magnitudes is the present constant.

Links

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

Kevin Ryde, Iterations of the R5 Dragon Curve, see index "HBf".

Formula

Equals (6 + 2*sqrt(5) + 2*sqrt(17)) / 5.

Equals (sqrt(8*sqrt(5*17) + 88) + 6) / 5.

Largest root of 625*x^4 - 3000*x^3 + 1000*x^2 + 6240*x - 2736 = 0 (all roots are real).

Example

3.7436694412469800984922334098821413...

Mathematica

RealDigits[(6 + 2*Sqrt[5] + 2*Sqrt[17])/5, 10, 120][[1]] (* Amiram Eldar, Jun 15 2023 *)

Prog

(PARI) my(c=352+32*quadgen(5*17*4)); a_vector(len) = my(s=10^(len-2)); digits(sqrtint(floor(c*s^2)) + floor(12*s));

Crossrefs

Cf. A349009 (area).

Sequence in context: A266273 A341605 A256676 * A267412 A087941 A278389

Adjacent sequences: A349007 A349008 A349009 * A349011 A349012 A349013

Keyword

cons,nonn

Author

Kevin Ryde, Nov 06 2021

Status

approved