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A368645
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Decimal expansion of the Mertens constant M(4,1) arising in the formula for the sum of reciprocals of primes p == 1 (mod 4) (negated).
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3
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2, 8, 6, 7, 4, 2, 0, 5, 6, 2, 2, 6, 1, 7, 5, 1, 9, 8, 6, 5, 3, 9, 4, 5, 1, 4, 1, 4, 3, 9, 4, 2, 3, 8, 5, 7, 3, 6, 4, 2, 0, 4, 3, 6, 6, 2, 4, 6, 9, 3, 8, 9, 2, 0, 9, 5, 7, 9, 7, 8, 1, 8, 2, 4, 6, 0, 1, 4, 9, 1, 6, 6, 1, 8, 7, 2, 5, 7, 9, 5, 0, 4, 5, 5, 3, 7, 8, 4, 9, 9, 7, 9, 7, 7, 7, 8, 3, 4, 7, 1, 8, 8, 9, 2, 7
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OFFSET
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0,1
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COMMENTS
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Data were taken from Languasco and Zaccagnini's web site.
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 95.
Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, p. 205.
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LINKS
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FORMULA
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Equals lim_{x->oo} (Sum_{primes p == 1 (mod 4), p <= x} 1/p - log(log(x))/2).
Equals gamma/2 - log(4*K_1/sqrt(Pi)) + Sum_{prime p == 1 (mod 4)} (log(1-1/p) + 1/p), where gamma is Euler's constant (A001620) and K_1 is Landau-Ramanujan constant (A064533).
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EXAMPLE
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-0.28674205622617519865394514143942385736420436624693...
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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