A339745 Decimal expansion of Product_{n>=2} (1 - n^(-10)).

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

Offset

0,1

Links

Table of n, a(n) for n=0..105.

Formula

Equals (cosh(sqrt((5 - sqrt(5))/2)*Pi) + sin(sqrt(5)*Pi/2)) * (cosh(sqrt((5 + sqrt(5))/2)*Pi) - sin(sqrt(5)*Pi/2)) / (40*Pi^4).

Equals exp(Sum_{j>=1} (1 - zeta(10*j))/j).

Example

0.99900544248098947527378453585422724586059097385364736908229...

Maple

evalf((cosh(sqrt((5 - sqrt(5))/2)*Pi) + sin(sqrt(5)*Pi/2)) * (cosh(sqrt((5 + sqrt(5))/2)*Pi) - sin(sqrt(5)*Pi/2)) / (40*Pi^4), 100);

Mathematica

RealDigits[(Cosh[Sqrt[(5 - Sqrt[5])/2]*Pi] + Sin[Sqrt[5]*Pi/2]) * (Cosh[Sqrt[(5 + Sqrt[5])/2]*Pi] - Sin[Sqrt[5]*Pi/2]) / (40*Pi^4), 10, 100][[1]]

Prog

(PARI) exp(suminf(j=1, (1 - zeta(10*j))/j))
(PARI) prodinf(n=2, 1-1/n^10) \\ Michel Marcus, Dec 15 2020

Crossrefs

Cf. A109219, A175615, A175616, A175617, A175618, A175619.

Sequence in context: A139345 A231470 A109942 * A346929 A346927 A197149

Adjacent sequences: A339742 A339743 A339744 * A339746 A339747 A339748

Keyword

nonn,cons

Author

Vaclav Kotesovec, Dec 15 2020

Status

approved