A372911 - OEIS

A372911

Decimal expansion of Sum_{k>=0} (4^k + 1)/(8^k + 1).

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, 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, 2, 8, 4, 1, 9, 2, 5, 4, 1, 9, 1, 8, 9, 4, 9, 9, 0, 0

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..86.

EXAMPLE

2.0690623551484755026547276432029562579215235314183649...

MATHEMATICA

s = Sum[(4^k + 1)/(8^k + 1), {k, 0, 1000}];

d = N[s, 100]

First[RealDigits[d]]

(* or *)

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 *)

CROSSREFS

Cf. A372907, A372908, A372909, A372910.

Sequence in context: A058498 A358167 A348189 * A003076 A175478 A011123

Adjacent sequences: A372908 A372909 A372910 * A372912 A372913 A372914

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Jul 01 2024

STATUS

approved