A086727 Decimal expansion of Sum_{m>=0} 1/(6*m+1)^2.

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

Offset

1,3

References

László Fejes Tóth, Lagerungen in der Ebene, auf der Kugel und im Raum, 2nd. ed., Springer-Verlag, Berlin, Heidelberg, 1972; see p. 213.

Links

Table of n, a(n) for n=1..99.

Formula

Equals 3F2(1/6,1/6,1; 7/6,7/6 ; 1). - R. J. Mathar, Oct 24 2025

From Amiram Eldar, Jun 26 2026: (Start)

Equals Sum_{m>=0} 1/A016922(m).

Equals psi'(1/6)/36, where psi' is the first derivative of the digamma function.

Equals Integral_{x=0..1} log(x)/(x^6 - 1) dx. (End)

Example

1.036625363676379414366130532397066119134525594076402...

Mathematica

RealDigits[N[PolyGamma[1, 1/6]/36, 100]][[1]]

Prog

(PARI) psi'(1/6)/36 \\ Amiram Eldar, Jun 26 2026

Crossrefs

Cf. A016922, A086722-A086731.

Sequence in context: A091478 A239567 A198239 * A309496 A392646 A021277

Adjacent sequences: A086724 A086725 A086726 * A086728 A086729 A086730

Keyword

nonn,cons,changed

Author

N. J. A. Sloane, Jul 31 2003

Status

approved