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A349010
Decimal expansion of the perimeter of the convex hull around the R5 dragon fractal.
4
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, 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
KEYWORD
cons,nonn
AUTHOR
Kevin Ryde, Nov 06 2021
STATUS
approved