A372909 Decimal expansion of Sum_{k>=0} (2^k + 1)/(4^k + 1).

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, 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, 7, 1, 1, 5, 9, 9, 5, 7, 0, 9, 0, 9, 2, 9, 8, 3, 8

Offset

1,1

Links

Table of n, a(n) for n=1..85.

Example

2.16249326597070366937751944159918604837132718186280262...

Mathematica

s = Sum[(2^k + 1)/(4^k + 1), {k, 0, 1000}];
d = N[s, 100]
First[RealDigits[d]] (* valid for first 200 digits; for more, change 1000 to 2000, etc. *)
(* or *)
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 *)

Crossrefs

Cf. A372907, A372908, A372910, A372911.

Sequence in context: A306549 A198870 A359273 * A365048 A050457 A195441

Adjacent sequences: A372906 A372907 A372908 * A372910 A372911 A372912

Keyword

nonn,cons

Author

Clark Kimberling, Jun 12 2024

Status

approved