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A244045 Decimal expansion of the Greenfield-Nussbaum constant, a constant which is the term z(1) in the quadratic recurrence z(0)=1, z(n) = z(n-1)+z(n-2)^2, such that all terms of the bi-infinite sequence z(n) (n = ..., -2, -1, 0, 1, 2, ...) are positive. 0
1, 5, 0, 7, 8, 7, 4, 7, 5, 5, 3, 9, 2, 7, 7, 5, 4, 7, 7, 6, 6, 2, 4, 2, 2, 2, 7, 0, 7, 7, 0, 9, 0, 6, 5, 8, 5, 7, 0, 9, 1, 1, 8, 7, 0, 9, 6, 8, 9, 3, 0, 9, 0, 0, 3, 3, 8, 8, 1, 1, 3, 8, 7, 1, 8, 2, 0, 2, 2, 8, 9, 8, 4, 6, 7, 2, 3, 3, 0, 4, 9, 4, 0, 5, 4, 1, 0, 1, 4, 5, 6, 6, 8, 1, 5, 5, 7, 1, 0, 7, 7, 5, 9, 4, 6 (list; constant; graph; refs; listen; history; text; internal format)
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
Cf. A000278.
Sequence in context: A108745 A114124 A155827 * A084248 A201417 A147666
KEYWORD
nonn,cons
AUTHOR
STATUS
approved

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Last modified May 30 06:59 EDT 2024. Contains 372962 sequences. (Running on oeis4.)