A389275 Decimal expansion of Sum_{i>=2} 1/(i^12 - i^6).

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

Offset

0,4

Links

Jason Bard, Table of n, a(n) for n = 0..1002

Michael Ian Shamos, Shamos's Catalog of the Real Numbers, (2011). See p. 27.

Formula

Equals Sum_{i>=2} (zeta(6*i) - 1).

Equals 23/12 - Pi^6/945 - Pi*tanh(sqrt(3)*Pi/2)/(2*sqrt(3)). - Vaclav Kotesovec, Sep 28 2025

Example

0.00024996440087243649923867470703467230468685944789353...

Mathematica

RealDigits[Re[Sum[1/(i^12 - i^6), {i, 2, Infinity}]], 10, 100, -1][[1]]
(* or *)
Join[{0, 0, 0}, RealDigits[23/12 - Pi^6/945 - Pi*Tanh[Sqrt[3]*Pi/2]/(2*Sqrt[3]), 10, 105][[1]]] (* Vaclav Kotesovec, Sep 28 2025 *)

Crossrefs

Cf. A013664, A013670, A013676.

Sequence in context: A337911 A198679 A244285 * A111422 A279035 A076661

Adjacent sequences: A389272 A389273 A389274 * A389276 A389277 A389278

Keyword

nonn,cons

Author

Jason Bard, Sep 28 2025

Status

approved