%I #7 Jul 07 2024 21:07:04
%S 2,0,6,9,0,6,2,3,5,5,1,4,8,4,7,5,5,0,2,6,5,4,7,2,7,6,4,3,2,0,2,9,5,6,
%T 2,5,7,9,2,1,5,2,3,5,3,1,4,1,8,3,6,4,9,7,6,5,4,3,3,2,1,0,0,0,2,2,0,5,
%U 2,8,4,1,9,2,5,4,1,9,1,8,9,4,9,9,0,0
%N Decimal expansion of Sum_{k>=0} (4^k + 1)/(8^k + 1).
%e 2.0690623551484755026547276432029562579215235314183649...
%t s = Sum[(4^k + 1)/(8^k + 1), {k, 0, 1000}];
%t d = N[s, 100]
%t First[RealDigits[d]]
%t (* or *)
%t RealDigits[Chop[N[(Log[7] - Pi/Sqrt[3] + QPolyGamma[0, 1 - I*Pi/Log[2], 1/2] + QPolyGamma[0, 1 - I*Pi/(3*Log[2]), 1/8] + (-1)^(2/3)*QPolyGamma[0, 1 - I*Pi/(3*Log[2]), 2] - (-1)^(1/3)*QPolyGamma[0, 1 + I*Pi/(3*Log[2]), 2]) / (3*Log[2]) - 1/6, 120]], 10, 110][[1]] (* _Vaclav Kotesovec_, Jul 01 2024 *)
%Y Cf. A372907, A372908, A372909, A372910.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Jul 01 2024