A344778 Decimal expansion of 4 * Pi^5 / (729 * sqrt(3)).

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

Offset

0,1

References

L. B. W. Jolley, Summation of Series, Dover, 1961, Eq. (310).

Links

Table of n, a(n) for n=0..86.

Michael I. Shamos, Shamos's catalog of the real numbers (2011).

Index entries for transcendental numbers.

Formula

Equals 2^2 * Pi^5 / (3^6 * sqrt(3)).

Equals 1 + Sum_{k>=1} ( 1/(3*k+1)^5 - 1/(3*k-1)^5 ).

Equals Product_{p prime} (1 - Kronecker(-3, p)/p^5)^(-1) = Product_{p prime != 3} (1 + (-1)^(p mod 3)/p^5)^(-1). - Amiram Eldar, Nov 06 2023

Example

0.969440589235153201449724794946430940...

Mathematica

RealDigits[(4 Pi^5)/(729Sqrt[3]), 10, 120][[1]] (* Harvey P. Dale, Mar 09 2023 *)

Crossrefs

Cf. A129404, A344727, A344688.

Sequence in context: A155533 A083281 A019711 * A010545 A197506 A225452

Adjacent sequences: A344775 A344776 A344777 * A344779 A344780 A344781

Keyword

nonn,cons

Author

Sean A. Irvine, Aug 17 2021

Status

approved