

A175646


Decimal expansion of the Product_{primes p == 1 (mod 3)} 1/(11/p^2).


14



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, 8, 9, 0, 9, 9, 8, 8, 6, 4, 1, 6, 8, 2, 5, 0, 3, 8, 4, 2, 1, 2, 2, 2, 2, 4, 5, 8, 7, 1, 0, 9, 6, 3, 5, 8, 0, 4, 9, 6, 2, 1, 7, 0, 7, 9, 8, 2, 6, 2, 0, 5, 9, 6, 2, 8, 9, 9, 7
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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 (11/7^2)*(11/13^2)*(11/19^2)*...
There is a complementary product_{primes == 2 mod 3} 1/(11/p^2) = A333240 = 1.4140643908921476375655018190798... such that (this constant here)*1.4140643.../(11/3^2) = zeta(2) = A013661.
Because 1/(1p^(2)) = 1+1/(p^21), the complementary 1.414064.. equals also Product_{primes p == 2 (mod 3)} (1+1/(p^21)), which appears in Eq. (1.8) of [Dence and Pomerance].  R. J. Mathar, Jan 31 2013


LINKS

Table of n, a(n) for n=1..105.
Thomas Dence and Carl Pomerance, Euler's Function in Residue Classes, Raman. J., Vol. 2 (1998) pp. 720, alternative link.
R. J. Mathar, Table of Dirichlet Lseries and Prime Zeta Modulo Functions for Small Moduli, arXiv:1008.2547 [math.NT], 20102015, p. 26.


FORMULA

Equals 2*Pi^2 / (3^(7/2) * A301429^2).  Vaclav Kotesovec, May 12 2020
Equals Sum_{k>=1} 1/A004611(k)^2.  Amiram Eldar, Sep 27 2020


EXAMPLE

1.03401487541434188053903064441304762857896..


CROSSREFS

Cf. A002476, A004611, A007528, A175647, A334478, A334480.
Sequence in context: A021298 A170952 A194587 * A324362 A073234 A123685
Adjacent sequences: A175643 A175644 A175645 * A175647 A175648 A175649


KEYWORD

cons,nonn,changed


AUTHOR

R. J. Mathar, Aug 01 2010


EXTENSIONS

More digits from Vaclav Kotesovec, May 12 2020 and Jun 27 2020


STATUS

approved



