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A244645
Decimal expansion of the sum of the reciprocals of the octagonal numbers (A000567).
8
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
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
KEYWORD
nonn,cons,easy
AUTHOR
Robert G. Wilson v, Jul 03 2014
STATUS
approved