%I
%S 1,0,2,1,6,5,1,2,4,7,5,3,1,9,8,1,3,6,6,4,1,1,0,2,8,1,9,2,6,0,7,3,2,3,
%T 8,6,9,7,5,6,2,2,1,5,9,2,8,9,1,5,3,6,5,4,0,3,5,5,9,0,7,1,1,5,6,7,3,3,
%U 6,9,3,8,8,9,7,8,0,9,7,5,9,5,5,1,3,0,3,6,2,4,6,5,5,8,8,9,5,0,4,4
%N Decimal expansion of 2*Log[5/3] = 1.0216... used by BBP Pi formula.
%C Equals 2*Log[5/3] = 2(Log[5]Log[3]) = Log[25/9] = 4 ArcTanh[1/4] =
%C Hypergeometric2F1[1, 1/2, 3/2, 1/16] = Sum[(1/16)^n (1/(2n+1)),{n,0,Infinity}]
%C BBP Formula on Pi = 4*A145963(1/2)A145960(1/2)A145961A145962 =
%C (*Artur Jasinski*) =4((1/16) (Pi + 4 ArcTan[1/3] + 4 Sqrt[2] ArcTan[1/Sqrt[2]] + Log[25]  2 Sqrt[2] Log[2  Sqrt[2]] + 2 Sqrt[2] Log[2 + Sqrt[2]]))
%C (Sqrt[2] ArcCot[Sqrt[2]] + Sqrt[2] ArcCoth[Sqrt[2]]  Log[5]/2  Pi/4  ArcCot[3])
%C (1/2)(2*Log[5/3])
%C (1/2)(2*Log[3]2 ArcTan[1/2]) =
%C Pi = 3.1414... = A000796
%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/BBPFormula.html">BBP Formula</a>
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%t First[RealDigits[2 Log[5/3], 10, 100]]
%o (PARI) 2*log(5/3) \\ _Michel Marcus_, Apr 05 2015
%Y Cf. A000796, A145961, A145962, A145963.
%K cons,nonn
%O 1,3
%A _Artur Jasinski_, Oct 25 2008
