OFFSET
1,2
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 6.10 Quadratic recurrence constants, p. 446.
LINKS
Stephen J. Greenfield and Roger D. Nussbaum, Dynamics of a Quadratic Map in Two Complex Variables
EXAMPLE
1.5078747553927754776624222707709065857...
MATHEMATICA
digits = 105; n0 = 10; dn = 10; init[z1_] := (Clear[z]; z[0] = 1; z[1] = z1; z[n_?Positive] := z[n] = z[n-1] + z[n-2]^2; z[n_?Negative] := z[n] = Sqrt[z[n+2] - z[n+1]]); g[z1_?NumericQ, n_] := (init[z1]; Table[z[k], {k, -n, -1}] // Im // Norm); Clear[f]; f[n_] := f[n] = z1 /. FindMinimum[g[z1, n], {z1, 3/2}, WorkingPrecision -> 3*digits][[2]]; f[n0]; f[n = n0 + dn]; While[ RealDigits[f[n], 10, digits] != RealDigits[f[n - dn], 10, digits], Print["n = ", n]; n = n + dn]; RealDigits[f[n], 10, digits] // First
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Jun 18 2014
STATUS
approved