

A199401


Decimal expansion of constant Product_{p>=3} (1  (1)^((p1)/2)/(p1)).


3



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
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OFFSET

1,2


COMMENTS

Arises in studying A002496.
From R. J. Mathar, Nov 29 2011: (Start)
The constant is Product_{primes p} (1chi(p)/(p1)) 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)


REFERENCES

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). 170. See Section 5.41.


LINKS

Table of n, a(n) for n=1..29.
T. Amdeberhan, L. A. Median, V. H. Moll, Arithmetical properties of a sequence arising from an arctangent sum, J. Numb. Theory 128 (2008) 18071846, eq. (1.10).
Marek Wolf, Search for primes of the form m^2+1


EXAMPLE

1.372813462818246009112192696727...


CROSSREFS

Cf. A002496.
Sequence in context: A279341 A254155 A211342 * A261573 A159759 A243964
Adjacent sequences: A199398 A199399 A199400 * A199402 A199403 A199404


KEYWORD

nonn,cons,more


AUTHOR

N. J. A. Sloane, Nov 05 2011


STATUS

approved



