login
A343487
Decimal expansion of the perimeter of the convex hull around the terdragon fractal.
2
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, 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
KEYWORD
cons,easy,nonn
AUTHOR
Kevin Ryde, Apr 17 2021
STATUS
approved