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A249272
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Decimal expansion of a constant associated with fundamental discriminants and Dirichlet characters.
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0
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4, 9, 8, 0, 9, 4, 7, 3, 3, 9, 6, 1, 4, 9, 3, 4, 1, 5, 0, 7, 9, 1, 3, 2, 5, 3, 2, 5, 8, 8, 0, 7, 7, 5, 2, 8, 1, 2, 3, 7, 7, 3, 2, 6, 9, 6, 5, 8, 5, 2, 0, 4, 7, 9, 5, 4, 6, 2, 3, 3, 1, 2, 7, 1, 8, 6, 7, 3, 3, 2, 6, 3, 8, 1, 9, 6, 8, 0, 0, 3, 8, 1, 5, 2, 0, 9, 0, 4, 7, 7, 4, 9, 0, 0, 6, 1, 7, 6, 1, 6, 2, 1, 2
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OFFSET
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1,1
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LINKS
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Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 250.
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FORMULA
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sum_{q} q^2/(2(q+1)) prod_{p<q} (p+2)/(2(p+1)), where p, q are primes.
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EXAMPLE
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4.9809473396149341507913253258807752812377326965852...
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MATHEMATICA
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digits = 103; Clear[s, P]; P[j_] := P[j] = Product[(Prime[k] + 2)/(2*(Prime[k] + 1)), {k, 1, j - 1}] // N[#, digits + 100]&; s[m_] := s[m] = Sum[Prime[j]^2/(2*(Prime[j] + 1))*P[j], {j, 1, m}]; s[10]; s[m = 20]; While[RealDigits[s[m]] != RealDigits[s[m/2]], Print[m, " ", N[s[m]]]; m = 2*m]; RealDigits[s[m], 10, digits] // First
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PROG
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(PARI) suminf(k=1, prime(k)^2/(2*(prime(k)+1))*prod(i=1, k-1, (prime(i)+2)/(2*(prime(i)+1)))); \\ Michel Marcus, Apr 15 2017
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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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