cp's OEIS Frontend

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

%I A349010 #13 Jun 15 2023 02:31:09
%S A349010 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,
%T A349010 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,
%U A349010 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
%N A349010 Decimal expansion of the perimeter of the convex hull around the R5 dragon fractal.
%C A349010 The fractal is taken scaled to unit length from curve start to end.
%C A349010 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.
%H A349010 Kevin Ryde, <a href="/A349010/b349010.txt">Table of n, a(n) for n = 1..10000</a>
%H A349010 Kevin Ryde, <a href="http://user42.tuxfamily.org/r5dragon/index.html">Iterations of the R5 Dragon Curve</a>, see index "HBf".
%F A349010 Equals (6 + 2*sqrt(5) + 2*sqrt(17)) / 5.
%F A349010 Equals (sqrt(8*sqrt(5*17) + 88) + 6) / 5.
%F A349010 Largest root of 625*x^4 - 3000*x^3 + 1000*x^2 + 6240*x - 2736 = 0 (all roots are real).
%e A349010 3.7436694412469800984922334098821413...
%t A349010 RealDigits[(6 + 2*Sqrt[5] + 2*Sqrt[17])/5, 10, 120][[1]] (* _Amiram Eldar_, Jun 15 2023 *)
%o A349010 (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));
%Y A349010 Cf. A349009 (area).
%K A349010 cons,nonn
%O A349010 1,1
%A A349010 _Kevin Ryde_, Nov 06 2021