A340808 Decimal expansion of Product_{primes p == 1 (mod 5)} 1/(1-p^(-4)).

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

Offset

1,6

Comments

Equals also the same product over the primes p == 1 (mod 10).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..500

R. J. Mathar, Table of Dirichlet L-series and prime zeta modulo functions... arXiv:1008.2547, Zeta_{m=5,n=1}(s=4).

Formula

A340629 = A340004 ^2 / this.

Equals Sum_{k>=1} 1/A004615(k)^4. - Amiram Eldar, Jan 24 2021

Example

1.0000698728321842614141963526460062515  = (14641/14640) * (923521/923520) * (2825761/2825760) *...

Crossrefs

Cf. A004615, A030430, A340004 (s=2), A340629, A340809, A340926, A340927.

Sequence in context: A198557 A338699 A198214 * A233589 A199282 A133614

Adjacent sequences: A340805 A340806 A340807 * A340809 A340810 A340811

Keyword

nonn,cons

Author

R. J. Mathar, Jan 22 2021

Extensions

More digits from Vaclav Kotesovec, Jan 22 2021

Status

approved