cp's OEIS Frontend

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

%I A343487 #13 Dec 25 2021 12:08:07
%S A343487 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,
%T A343487 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,
%U A343487 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
%N A343487 Decimal expansion of the perimeter of the convex hull around the terdragon fractal.
%C A343487 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.
%H A343487 Kevin Ryde, <a href="/A343487/b343487.txt">Table of n, a(n) for n = 1..10000</a>
%H A343487 Kevin Ryde, <a href="http://user42.tuxfamily.org/terdragon/index.html">Iterations of the Terdragon Curve</a>, see index "HBf".
%F A343487 Equals (13 + 5*sqrt(3) + 2*sqrt(37)) / 12.
%F A343487 Equals (13 + sqrt(223 + 20*sqrt(3*37))) / 12.
%F A343487 Largest root of ((12*x - 13)^2 - 223)^2 - 44400 = 0 (all its roots are real).
%e A343487 2.8188149248700688204697166831611246...
%t A343487 RealDigits[(13+5*Sqrt[3]+2*Sqrt[37])/12,10,120][[1]] (* _Harvey P. Dale_, Dec 25 2021 *)
%o A343487 (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);
%Y A343487 Cf. A343486 (terdragon hull area), A341030 (dragon hull perimeter).
%K A343487 cons,easy,nonn
%O A343487 1,1
%A A343487 _Kevin Ryde_, Apr 17 2021