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A175647 Decimal expansion of the product_{primes ==1 mod 4} 1/(1-1/p^2). 3
1, 0, 5, 6, 1, 8, 2, 1, 2, 1, 7, 2, 6, 8, 1, 6, 1, 4, 1, 7, 3, 7, 9, 3, 0, 7, 6, 5, 3, 1, 6, 2, 1, 9, 8, 9, 0, 5, 8, 7, 5, 8, 0, 4, 2, 5, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The Euler product of the Riemann zeta function at 2 restricted to primes in A002144, which is the inverse of the infinite product (1-1/5^2)*(1-1/13^2)*(1-1/17^2)*(1-1/29^2)*...

There is a complementary product_{primes == 3 mod 4} 1/(1-1/p^2) = 1.16807558541051428866969673706404040136467... such that (this constant here)*1.16807.../(1-1/2^2) = zeta(2) = A013661.

LINKS

Table of n, a(n) for n=1..47.

R. J. Mathar, Table of Dirichlet L-series and Prime Zeta Modulo Functions for Small Moduli, arXiv:1008.2547 [math.NT]

EXAMPLE

1.0561821217268161417379307653162198905...

CROSSREFS

Cf. A175646.

Sequence in context: A195449 A020798 A021182 * A113262 A131947 A195823

Adjacent sequences:  A175644 A175645 A175646 * A175648 A175649 A175650

KEYWORD

cons,nonn

AUTHOR

R. J. Mathar, Aug 01 2010

EXTENSIONS

Link replaced by more permanent arXiv URL - R. J. Mathar, Sep 20 2010

STATUS

approved

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Last modified November 29 00:35 EST 2014. Contains 250479 sequences.