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A199401 Decimal expansion of constant Product_{p>=3} (1 - (-1)^((p-1)/2)/(p-1)). 3


%S 1,3,7,2,8,1,3,4,6,2,8,1,8,2,4,6,0,0,9,1,1,2,1,9,2,6,9,6,7

%N Decimal expansion of constant Product_{p>=3} (1 - (-1)^((p-1)/2)/(p-1)).

%C Arises in studying A002496.

%C From _R. J. Mathar_, Nov 29 2011: (Start)

%C The constant is Product_{primes p} (1-chi(p)/(p-1)) where chi is the Dirichlet character A101455. Its Euler expansion is (1/(L(m=4,r=2,s=1)* zeta(m=4,n=3,s=2)) *Product_{s>=2} zeta(m=4,n=1,s)^gamma(s), where L and zeta are the functions tabulated in arXiv:1008.2547 and gamma is the sequence A001037. In particular L(m=4,r=2,s=1) = A003881 and zeta(m=4,n=1,s=2)=A175647. (End)

%D G. H. Hardy and J. E. Littlewood. Some problems of Partitio Numerorum III: On the expression of a number as a sum of primes. Acta Mathematica, 44 (1922). 1-70. See Section 5.41.

%H T. Amdeberhan, L. A. Median, V. H. Moll, <a href="http://dx.doi.org/10.1016/j.jnt.2007.05.008">Arithmetical properties of a sequence arising from an arctangent sum</a>, J. Numb. Theory 128 (2008) 1807-1846, eq. (1.10).

%H Marek Wolf, <a href="http://arXiv.org/abs/0803.1456">Search for primes of the form m^2+1</a>

%e 1.372813462818246009112192696727...

%Y Cf. A002496.

%K nonn,cons,more

%O 1,2

%A _N. J. A. Sloane_, Nov 05 2011

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