A334479 Decimal expansion of Product_{k>=1} (1 + 1/A007528(k)^3).

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

Offset

1,4

Comments

In general, for s > 0, Product_{k>=1} (1 + 1/A007528(k)^(2*s+1)) / (1 - 1/A007528(k)^(2*s+1)) = (1 - 1/2^(2*s + 1)) * (3^(2*s + 1) - 1) * (2*s)! * zeta(2*s + 1) / (sqrt(3) * A002114(s) * Pi^(2*s + 1)).

For s > 1, Product_{k>=1} (1 + 1/A007528(k)^s) / (1 - 1/A007528(k)^s) = (2^s - 1) * (3^s - 1) * zeta(s) / (zeta(s, 1/6) - zeta(s, 5/6)).

For s > 1, Product_{k>=1} (1 + 1/A002476(k)^s) * (1 + 1/A007528(k)^s) = 6^s * zeta(s) / ((2^s + 1) * (3^s + 1) * zeta(2*s)).

Links

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

Formula

A334479 / A334480 = 91*sqrt(3)*zeta(3)/(6*Pi^3).

A334477 * A334479 = 810*zeta(3)/Pi^6.

Example

1.0091345086384744780711375395892055881745647852...

Crossrefs

Cf. A007528, A175646, A334424, A334426, A334480, A334482.

Sequence in context: A198835 A010167 A154181 * A239121 A019875 A248557

Adjacent sequences: A334476 A334477 A334478 * A334480 A334481 A334482

Keyword

nonn,cons

Author

Vaclav Kotesovec, May 02 2020

Extensions

More digits from Vaclav Kotesovec, Jun 27 2020

Status

approved