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 A181152 Decimal expansion of Madelung constant (negated) for the CsCl structure. 4
 1, 7, 6, 2, 6, 7, 4, 7, 7, 3, 0, 7, 0, 9, 8, 8, 3, 9, 7, 9, 3, 5, 6, 7, 3, 3, 2, 0, 6, 3, 8, 6, 4, 4, 2, 9, 1, 1, 7, 0, 5, 2, 8, 6, 1, 9, 5, 8, 8, 5, 8, 5, 2, 8, 0, 6, 4, 9, 4, 1, 8, 4, 3, 7, 7, 2, 7, 9, 6, 6, 2, 2, 3, 7, 6, 9, 3, 4, 0, 8, 3, 0, 4, 7, 1, 5, 0, 9, 4, 5, 8, 1, 1, 2, 1, 6, 9, 8, 8, 9, 0, 8, 5, 6, 9 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This is often quoted for a different lattice constant and multiplied by 2/sqrt(3) = 1.1547... = 10*A020832, which gives 1.76267...*1.1547... = 2.03536151... given in Zucker's Table 5 as the alpha for the CsCl structure, and by Sakamoto as the M_d for the B2 lattice. Given Zucker's b(1) = 0.774386141424002815... = A185577, this constant here is sqrt(3)*(3*b(1)+A085469)/4. - R. J. Mathar, Jan 28 2011 The CsCl structure consists of two interpenetrating simple cubic lattices of ions with charges +1 and -1, together occupying all the sites of the body-centered cubic lattice. - Andrey Zabolotskiy, Oct 21 2019 LINKS Leslie Glasser, Solid-State Energetics and Electrostatics: Madelung Constants and Madelung Energies, Inorg. Chem., 2012, 51 (4), 2420-2424. Y. Sakamoto, Madelung Constants of Simple Crystals ..., Journal of Chemical Physics, 28 (1958), 164-5.  Errata: J. Chem. Phys, 28 (1958), 733; J. Chem. Phys, 28 (1958), 1253. Nicolas Tavernier, Gian Luigi Bendazzoli, Véronique Brumas, Stefano Evangelisti, J. A. Berger, Clifford boundary conditions: a simple direct-sum evaluation of Madelung constants, arXiv:2006.01259 [physics.comp-ph], 2020. I. J. Zucker, Madelung constants and lattice sums for invariant cubic lattice complexes and certain tetragonal structures, J. Phys. A: Math. Gen. 8 (11) (1975) 1734. Wikipedia, Madelung constant MATHEMATICA digits = 105; m0 = 50; (* initial number of terms *) dm = 10; (* number of terms increment *) dd = 10; (* precision excess *) Clear[f]; f[n_, p_] := f[n, p] = (s = Sqrt[n^2 + p^2]; ((2 + (-1)^n) Csch[s*Pi])/s // N[#, digits + dd]&); f[m_] := f[m] = Pi/2 - (7 Log[2])/2 + 4 Sum[f[n, p], {n, 1, m}, {p, 1, m}]; f[m = m0]; f[m += dm]; While[Abs[f[m] - f[m - dm]] > 10^(-digits - dd), Print["f(", m, ") = ", f[m]]; m += dm]; A185577 = f[m]; Clear[g]; g[m_] := g[m] = 12 Pi Sum[Sech[(Pi/2) Sqrt[(2 j + 1)^2 + (2 k + 1)^2]]^2, {j, 0, m}, {k, 0, m}] // N[#, digits + dd]&; g[m = m0]; g[m += dm]; While[Abs[g[m] - g[m - dm]] > 10^(-digits - dd), Print["g(", m, ") = ", g[m]]; m += dm]; A085469 = g[m]; A181152 = Sqrt[3] (A085469 - 3 A185577)/4; RealDigits[A181152, 10, digits][[1]] (* Jean-François Alcover, May 07 2021 *) CROSSREFS Cf. A085469, A088537, A090734. Sequence in context: A323098 A068469 A276459 * A244920 A073011 A086312 Adjacent sequences:  A181149 A181150 A181151 * A181153 A181154 A181155 KEYWORD nonn,cons AUTHOR Leslie Glasser, Jan 24 2011 EXTENSIONS More terms (using the above comment from R. J. Mathar and terms from the b-files for A085469 and A185577) from Jon E. Schoenfield, Mar 10 2018 Definition corrected by Andrey Zabolotskiy, Oct 21 2019 a(88)-a(105) from Jean-François Alcover, May 07 2021 STATUS approved

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Last modified June 23 13:50 EDT 2021. Contains 345402 sequences. (Running on oeis4.)