A244647 Decimal expansion of the sum of the reciprocals of the decagonal numbers (A001107).

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

Offset

1,2

Comments

For the partial sums of the reciprocals of the (positive) decagonal numbers see A250551(n+1)/A294515(n), n >= 0. - Wolfdieter Lang, Nov 07 2017

Links

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

Wikipedia, Polygonal number

Formula

Sum_{n>0} 1/(4n^2 - 3n) = log(2) + Pi/6, (A002162 + A019673).

Example

1.216745956158244182494339352004760382108361700922772890949837441544696356350....

Mathematica

RealDigits[ Log[2] + Pi/6, 10, 111][[1]] (* or *)
RealDigits[ Sum[1/(4n^2 - 3n), {n, 1 , Infinity}], 10, 111][[1]]

Prog

(PARI) log(2)+Pi/6 \\ Charles R Greathouse IV, Feb 08 2023

Crossrefs

Cf. A001107, A000038, A013661, A244639, A016627, A244645, A244646, A244648, A244649, A250551(n+1)/A294515(n).

Sequence in context: A258870 A217922 A196554 * A324037 A160348 A047708

Adjacent sequences: A244644 A244645 A244646 * A244648 A244649 A244650

Keyword

nonn,cons,easy

Author

Robert G. Wilson v, Jul 03 2014

Status

approved