A244645 Decimal expansion of the sum of the reciprocals of the octagonal numbers (A000567).

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

Offset

1,2

Links

Table of n, a(n) for n=1..105.

Lawrence Downey, Boon W. Ong, and James A. Sellers, Beyond the Basel Problem: Sums of Reciprocals of Figurate Numbers, Coll. Math. J., 39, no. 5 (2008), 391-394.

Wikipedia, Polygonal number

Formula

Equals Sum_{n>=1} 1/(3*n^2 - 2*n).

Equals Pi/(4*sqrt(3)) + 3*log(3)/4. - Vaclav Kotesovec, Jul 05 2014

Example

1.2774090575596367311949534921024332115566344803902472326934919840751515151955452...

Mathematica

RealDigits[ Sum[1/(3n^2 - 2n), {n, 1 , Infinity}], 10, 111][[1]]

Prog

(PARI) sumpos(n=1, 1/(3*n^2 - 2*n)) \\ Michel Marcus, Sep 12 2016
(PARI) sumnumrat(1/(3*n-2)/n, 1) \\ Charles R Greathouse IV, Feb 08 2023

Crossrefs

Cf. A000038, A013661, A244639, A244644, A244646, A244647, A244648, A244649, A000567.

Sequence in context: A020770 A177003 A164767 * A277527 A188636 A344520

Adjacent sequences: A244642 A244643 A244644 * A244646 A244647 A244648

Keyword

nonn,cons,easy

Author

Robert G. Wilson v, Jul 03 2014

Status

approved