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

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

(PARI) (Pi*sqrt(3)+9*log(3))/24
(Magma) SetDefaultRealField(RealField(139)); R:= RealField(); (Pi(R)*Sqrt(3)+9*Log(3))/24; // G. C. Greubel, Mar 24 2024
(SageMath) numerical_approx((pi*sqrt(3)+9*log(3))/24, digits=139) # G. C. Greubel, Mar 24 2024

Crossrefs

Cf. A000217, A000796, A002194, A002391, A051865.

Cf. A244639, A244641, A244645, A244646, A244647, A244648, A244649.

Sequence in context: A307731 A193080 A197135 * A088246 A179559 A086648

Adjacent sequences: A365519 A365520 A365521 * A365523 A365524 A365525

Keyword

nonn,cons

Author

Claude H. R. Dequatre, Sep 08 2023

Status

approved