A340926 -id:A340926 - cp's OEIS frontend

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

R. J. Mathar, Jan 22 2021

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

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

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).

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

A340629 = A340004 ^2 / this.

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

More digits from Vaclav Kotesovec, Jan 22 2021

A340809 Decimal expansion of Product_{primes p == 4 (mod 5)} 1/(1-p^(-4)).

Original entry on oeis.org

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

Offset: 1

R. J. Mathar, Jan 22 2021

Equals also the same product over the primes p==9 (mod 10).

			1.0000092261581025751416880414384715475110104...

Vaclav Kotesovec, Table of n, a(n) for n = 1..500
R. J. Mathar, Table of Dirichlet L-series and prime zeta modulo functions for small moduli, arXiv:1008.2547 [math.NT], 2010-2015, Zeta_{m=5,n=4}(s=4).

Cf. A004618, A030433, A340127 (s=2), A340628, A340808, A340926, A340927.

Equals A340127 ^2/A340628

Equals Sum_{k>=1} 1/A004618(k)^4. - Amiram Eldar, Jan 24 2021

More digits from Vaclav Kotesovec, Jan 22 2021

A340927 Decimal expansion of Product_{primes p == 3 (mod 5)} 1/(1 - 1/p^4).

Original entry on oeis.org

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

Offset: 1

Vaclav Kotesovec, Jan 27 2021

			1.012539571644935903522100272691152140478362802787749854800134772695303...

Vaclav Kotesovec, Table of n, a(n) for n = 1..500
R. J. Mathar, Table of Dirichlet L-series and Prime Zeta Modulo Functions for Small Moduli, arXiv:1008.2547 [math.NT], 2010-2015, Zeta_{m=5,n=3}(s=4).

Cf. A340808, A340809, A340926.
Cf. A340004, A340794, A340665, A340127.
Cf. A340629, A340710, A340711, A340628.

Equals A340665^2 / A340711.
Equals 104*Pi^4 / (9375 * A340808 * A340926 * A340809).
Equals Sum_{k>=1} 1/A004617(k)^4. - Amiram Eldar, Jan 28 2021

cp's OEIS Frontend

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

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A340809 Decimal expansion of Product_{primes p == 4 (mod 5)} 1/(1-p^(-4)).

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A340927 Decimal expansion of Product_{primes p == 3 (mod 5)} 1/(1 - 1/p^4).

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