A389777 - OEIS

A389777

Decimal expansion of Sum_{k>=2} 1/(k^10 - k^2).

0, 0, 0, 9, 9, 8, 4, 0, 7, 3, 8, 1, 0, 7, 3, 8, 9, 9, 7, 6, 7, 1, 2, 6, 8, 4, 8, 9, 1, 6, 3, 3, 9, 1, 5, 0, 2, 3, 5, 6, 7, 7, 5, 6, 4, 5, 9, 0, 4, 9, 6, 6, 4, 6, 1, 3, 6, 5, 2, 4, 3, 6, 2, 8, 5, 5, 5, 9, 3, 8, 8, 5, 8, 7, 1, 6, 4, 7, 3, 0, 2, 8, 9, 4, 7, 8, 9, 5, 6, 2, 4, 8, 3, 1, 1, 5, 0, 5, 5, 4

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OFFSET

0,4

LINKS

Jason Bard, Table of n, a(n) for n = 0..5002

Michael I. Shamos, Shamos's Catalog of the Real Numbers, 2011, p. 28.

FORMULA

Equals 11/16 - Pi^2/6 + Pi*coth(Pi)/8 + Pi*(sin(sqrt(2)*Pi) - sinh(sqrt(2)*Pi)) / (4*sqrt(2)*(cos(sqrt(2)*Pi) - cosh(sqrt(2)*Pi))). - Vaclav Kotesovec, Oct 15 2025

EXAMPLE

0.000998407381073899767126848916339150235677564590496646...

MATHEMATICA

First[RealDigits[Re[Sum[1/(k^10 - k^2), {k, 2, Infinity}]], 10, 100, -1]]

RealDigits[11/16 - Pi^2/6 + Pi*Coth[Pi]/8 + Pi*(Sin[Sqrt[2]*Pi] - Sinh[Sqrt[2]*Pi]) / (4*Sqrt[2]*(Cos[Sqrt[2]*Pi] - Cosh[Sqrt[2]*Pi])), 10, 100, -1][[1]] (* Vaclav Kotesovec, Oct 15 2025 *)

CROSSREFS

Sequence in context: A300284 A347057 A334446 * A051554 A146493 A347055

Adjacent sequences: A389774 A389775 A389776 * A389778 A389779 A389780

KEYWORD

nonn,cons

AUTHOR

Jason Bard, Oct 14 2025

STATUS

approved