%I #10 Jul 01 2024 04:48:51
%S 2,1,6,2,4,9,3,2,6,5,9,7,0,7,0,3,6,6,9,3,7,7,5,1,9,4,4,1,5,9,9,1,8,6,
%T 0,4,8,3,7,1,3,2,7,1,8,1,8,6,2,8,0,2,6,2,8,0,5,8,4,9,9,7,1,1,5,9,2,7,
%U 7,1,1,5,9,9,5,7,0,9,0,9,2,9,8,3,8
%N Decimal expansion of Sum_{k>=0} (2^k + 1)/(4^k + 1).
%e 2.16249326597070366937751944159918604837132718186280262...
%t s = Sum[(2^k + 1)/(4^k + 1), {k, 0, 1000}];
%t d = N[s, 100]
%t First[RealDigits[d]] (* valid for first 200 digits; for more, change 1000 to 2000, etc. *)
%t (* or *)
%t RealDigits[Chop[N[-1 + (Log[3] - Pi + QPolyGamma[0, -I*Pi/Log[4], 1/4] + I*QPolyGamma[0, -I*Pi/Log[4], 2] - I*QPolyGamma[0, I*Pi/Log[4], 2])/Log[4], 120]], 10, 110][[1]] (* _Vaclav Kotesovec_, Jun 13 2024 *)
%Y Cf. A372907, A372908, A372910, A372911.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Jun 12 2024