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A175646 Decimal expansion of the product_{primes ==1 mod 3} 1/(1-1/p^2). 2
1, 0, 3, 4, 0, 1, 4, 8, 7, 5, 4, 1, 4, 3, 4, 1, 8, 8, 0, 5, 3, 9, 0, 3, 0, 6, 4, 4, 4, 1, 3, 0, 4, 7, 6, 2, 8, 5, 7, 8, 9, 6, 5, 4, 2, 8, 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 A002476, which is the inverse of the infinite product (1-1/7^2)*(1-1/13^2)*(1-1/19^2)*...

There is a complementary product_{primes == 2 mod 3} 1/(1-1/p^2) = 1.4140643908921476375655018190798... such that (this constant here)*1.4140643.../(1-1/3^2) = zeta(2) = A013661.

Because 1/(1-p^(-2)) = 1+1/(p^2-1), the complementary 1.414064.. equals also product_{primes ==2 mod 3} (1+1/(p^2-1)), which appears in Eq. (1.8) of [Dence, Pomerance]. R. J. Mathar, Jan 31 2013

LINKS

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

T. Dence, C. Pomerance, Euler's Function in Residue Classes, Raman. J. 2 (1998) 7-20.

R. J. Mathar, Table of Dirichlet L-series and Prime Zeta Modulo Functions for Small Moduli, arXiv:1008.2547 [math.NT], p 26.

EXAMPLE

1.03401487541434188053903064441304762857896..

CROSSREFS

Cf. A175647.

Sequence in context: A021298 A170952 A194587 * A324362 A073234 A123685

Adjacent sequences:  A175643 A175644 A175645 * A175647 A175648 A175649

KEYWORD

cons,nonn

AUTHOR

R. J. Mathar, Aug 01 2010

STATUS

approved

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Last modified March 25 04:25 EDT 2019. Contains 321457 sequences. (Running on oeis4.)