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 A247046 Decimal expansion of delta_3, a constant associated with a certain 3-dimensional lattice sum. 1
 2, 3, 1, 3, 6, 9, 8, 7, 0, 3, 8, 8, 2, 3, 2, 0, 6, 0, 3, 5, 8, 8, 8, 0, 9, 8, 7, 4, 0, 6, 1, 1, 5, 5, 0, 0, 8, 3, 5, 6, 3, 5, 7, 1, 3, 5, 5, 9, 5, 9, 6, 5, 9, 6, 2, 1, 7, 4, 5, 6, 1, 5, 7, 4, 9, 4, 7, 9, 4, 4, 9, 7, 6, 7, 8, 1, 2, 3, 8, 4, 7, 6, 3, 6, 9, 3, 6, 9, 0, 5, 9, 9, 0, 2, 3, 5, 8, 1, 9, 0 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 1.10 Madelung's constant, p. 79. LINKS Eric Weisstein's MathWorld, Lattice Sum FORMULA Pi_0 + Pi/6, where Pi_0 is A185576. EXAMPLE -2.313698703882320603588809874061155008356357135595965962... MATHEMATICA digits = 100; k0 = 10; dk = 10; Clear[s]; s[k_] := s[k] = 7*(Pi/6) - 19/2*Log[2] + 4*Sum[(3 + 3*(-1)^m + (-1)^(m + n))*Csch[Pi*Sqrt[m^2 + n^2]]/Sqrt[m^2 + n^2], {m, 1, k}, {n, 1, k}] // N[#, digits + 10] &; s[k0]; s[k = k0 + dk]; While[RealDigits[s[k], 10, digits + 5][[1]] != RealDigits[s[k - dk], 10, digits + 5][[1]], Print["s(", k, ") = ", s[k]]; k = k + dk]; Pi0 = s[k]; delta3 = Pi0 + Pi/6; RealDigits[delta3, 10, digits] // First CROSSREFS Cf. A088537, A185576, A247042. Sequence in context: A176850 A208516 A111808 * A081422 A213742 A213743 Adjacent sequences:  A247043 A247044 A247045 * A247047 A247048 A247049 KEYWORD nonn,cons,easy AUTHOR Jean-François Alcover, Sep 10 2014 STATUS approved

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Last modified April 12 22:36 EDT 2021. Contains 342933 sequences. (Running on oeis4.)