A365522 - OEIS

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A365522

Decimal expansion of (Pi*sqrt(3) + 9*log(3))/24.

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

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OFFSET

0,1

COMMENTS

This sequence is also the decimal expansion of Sum_{k>=1} 1/(f(k) +g(k)), where f(k) and g(k) are respectively the k-th triangular and the 13-gonal numbers (A000217 and A051865).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

Michael Ian Shamos, A catalog of the real numbers (2011), p. 544.

Wikipedia, Polygonal number.

FORMULA

Equals Sum_{k>=1} 1/(6*k^2 - 4*k) [Shamos].

Equals - Integral_{x=0..1} log(1-x^6)/x^5 dx [Shamos].

EXAMPLE

0.63870452877981836559747674605121660577831724019512...

MATHEMATICA

RealDigits[(Pi*Sqrt[3] + 9*Log[3])/24, 10 , 100][[1]] (* Amiram Eldar, Sep 08 2023 *)

PROG