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A199401 Decimal expansion of constant Product_{p>=3} (1 - (-1)^((p-1)/2)/(p-1)). 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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Arises in studying A002496.

From R. J. Mathar, Nov 29 2011: (Start)

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)

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). 1-70. 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) 1807-1846, 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

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Last modified August 19 07:50 EDT 2018. Contains 313857 sequences. (Running on oeis4.)