A355978 Decimal expansion of Product_{k>=1} zeta(Prime(k)).

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

Offset

1,1

Links

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

Robert A. Van Gorder, Infinite Multiple Products over the Primes of Type Product Product (1 - p_n^{-p_m})^{-1} and Generalizations, Int. J. Contemp. Math. Sciences, Vol. 5, No. 31 (2010), pp. 1499-1504.

Formula

Equals Product_{m,n>=1} 1/(1-prime(n)^(-prime(m))) = Product_{m>=1} 1/(1-1/A053810(m)).

Example

2.06873599797165833786362198099404928341340749889767...

Mathematica

RealDigits[Product[Zeta[Prime[n]], {n, 1, 100}], 10, 100][[1]]

Crossrefs

Cf. A021002, A053810, A080729, A080730.

Sequence in context: A248507 A087996 A086777 * A334349 A058498 A358167

Adjacent sequences: A355975 A355976 A355977 * A355979 A355980 A355981

Keyword

nonn,cons

Author

Amiram Eldar, Jul 22 2022

Status

approved