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A199401
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Decimal expansion of constant Product_{p>=3} (1 - (-1)^((p-1)/2)/(p-1)). Hardy-Littlewood constant of x^2 + 1.
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4
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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, 2, 7, 0, 1, 8, 8, 6, 8, 1, 7, 8, 3, 3, 3, 1, 0, 1, 2, 5, 5, 7, 5, 9, 5, 5, 7, 9, 3, 6, 2, 3, 4, 1, 4, 7, 3, 2, 7, 8, 4, 2, 2, 2, 6, 7, 1, 7, 3, 7, 0, 2, 3, 1, 7, 2, 7, 7, 1
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OFFSET
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1,2
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COMMENTS
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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. - R. J. Mathar, Nov 29 2011
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LINKS
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EXAMPLE
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1.372813462818246009112192696727...
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PROG
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(PARI) See Belabas, Cohen link. Run as HardyLittlewood2(x^2+1) after setting the required precision.
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CROSSREFS
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Equals 2*constant given by A331941.
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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