The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A372911

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A372911

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

#7 by N. J. A. Sloane at Sun Jul 07 21:07:04 EDT 2024

STATUS

proposed

approved

#6 by Vaclav Kotesovec at Mon Jul 01 04:51:16 EDT 2024

STATUS

editing

proposed

#5 by Vaclav Kotesovec at Mon Jul 01 04:46:49 EDT 2024

MATHEMATICA

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

#4 by Vaclav Kotesovec at Mon Jul 01 04:46:21 EDT 2024

MATHEMATICA

(* 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 *)

STATUS

proposed

editing

#3 by Clark Kimberling at Mon Jul 01 00:18:45 EDT 2024

STATUS

editing

proposed

#2 by Clark Kimberling at Mon Jul 01 00:04:59 EDT 2024

NAME

allocated for Clark KimberlingDecimal expansion of Sum_{k>=0} (4^k + 1)/(8^k + 1).

DATA

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

OFFSET

1,1

EXAMPLE

2.0690623551484755026547276432029562579215235314183649...

MATHEMATICA

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

d = N[s, 100]

First[RealDigits[d]]

CROSSREFS

Cf. A372907, A372908, A372909, A372910.

KEYWORD

allocated

nonn,cons

AUTHOR

Clark Kimberling, Jul 01 2024

STATUS

approved

editing

#1 by Clark Kimberling at Thu May 16 03:59:16 EDT 2024

NAME

allocated for Clark Kimberling

KEYWORD

allocated

STATUS

approved