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A240943
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Decimal expansion of the radius of convergence of Wedderburn-Etherington numbers g.f.
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2
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4, 0, 2, 6, 9, 7, 5, 0, 3, 6, 7, 1, 4, 4, 1, 2, 9, 0, 9, 6, 9, 0, 4, 5, 3, 4, 8, 6, 5, 1, 0, 8, 3, 8, 0, 3, 4, 1, 7, 5, 5, 6, 7, 2, 1, 6, 2, 4, 9, 7, 2, 6, 5, 9, 2, 9, 1, 0, 5, 3, 4, 6, 4, 6, 0, 7, 6, 4, 2, 7, 2, 8, 9, 6, 6, 5, 2, 4, 2, 5, 8, 4, 1, 6, 4, 1, 6, 0, 9, 6, 0, 2, 6, 2, 1, 7, 2, 0, 5, 9, 5, 2
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OFFSET
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0,1
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.6 Otter's Tree Enumeration Constants, p. 297.
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LINKS
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FORMULA
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EXAMPLE
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0.4026975036714412909690453486510838034175567216249726592910534646...
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MATHEMATICA
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digits = 102; n0 = 50; dn = 50; Clear[rho]; rho[n_] := rho[n] = (Clear[c]; c[0] = 0; y[z_] = Sum[c[k]*z^k, {k, 0, n}]; eq[0] = Rest[ Thread[CoefficientList[(-2*z + 2*y[z] - y[z]^2 - y[z^2])/2, z] == 0]]; s[1] = First[Solve[First[eq[0]], c[1]]]; Do[eq[k-1] = Rest[eq[k-2]] /. s[k-1]; s[k] = First[Solve[First[eq[k-1]], c[k]]], {k, 2, n}]; z /. FindRoot[ 2*z + y[z^2] == 1 /. Flatten[Table[s[k], {k, 1, n}]], {z, 1/2}, WorkingPrecision -> digits+10]); rho[n0]; rho[n = n0 + dn]; While[RealDigits[rho[n], 10, digits] != RealDigits[rho[n - dn], 10, digits], Print["n = ", n]; n = n + dn]; RealDigits[rho[n], 10, digits] // First
(* or, after A086317: *) Clear[c, xi]; c[0] = 2; c[n_] := c[n] = c[n-1]^2 + 2; xi[n_Integer] := xi[n] = c[n]^(2^-n); xi[5]; xi[n = 10]; While[RealDigits[xi[n], 10, digits] != RealDigits[xi[n-5], 10, digits], n = n+5]; RealDigits[1/xi[n], 10, digits] // First (* Jean-François Alcover, Aug 04 2014 *)
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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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