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A245700 Decimal expansion of the expected distance from a randomly selected point in an equilateral triangle of side length 1 to a corner: (4+log(27))/12.

%I A245700 #19 Feb 16 2025 08:33:23
%S A245700 6,0,7,9,8,6,4,0,5,5,0,0,3,6,0,7,5,6,1,8,2,1,4,4,6,4,2,5,6,3,9,6,4,7,
%T A245700 5,9,4,9,5,2,0,5,9,7,2,7,8,9,0,2,0,6,9,6,2,6,7,0,0,6,9,1,6,7,4,2,7,0,
%U A245700 6,9,0,6,6,3,7,9,8,5,5,7,5,0,5,1,7,3,7,2,7,2,0,3,6,7,6,6,3,5,5,5,3,0,3,2,5,8,4,0,5,9,9,8,2,2,7,9,9,7,6
%N A245700 Decimal expansion of the expected distance from a randomly selected point in an equilateral triangle of side length 1 to a corner: (4+log(27))/12.
%H A245700 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TrianglePointPicking.html">Triangle Point Picking</a>.
%H A245700 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A245700 Equals Sum_{k>=1} k/((2*k-1)*2^(2*k-1)). - _Amiram Eldar_, May 27 2021
%e A245700 0.607986405500360756182144642563964759495205972789020696267006916742706906637985...
%t A245700 RealDigits[(4 + Log[27])/12, 10, 100][[1]] (* _Amiram Eldar_, May 27 2021 *)
%o A245700 (PARI) (4+log(27))/12 \\ _Charles R Greathouse IV_, Apr 20 2016
%Y A245700 Cf. A245698.
%K A245700 nonn,cons
%O A245700 0,1
%A A245700 _Derek Orr_, Jul 29 2014