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A240982
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Decimal expansion of the limit of a recursive sequence connected to the Plastic constant (A060006).
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0
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1, 8, 1, 6, 8, 8, 3, 4, 2, 4, 2, 4, 4, 7, 4, 0, 3, 1, 2, 4, 4, 8, 1, 8, 8, 2, 0, 2, 2, 2, 4, 8, 0, 7, 4, 5, 2, 9, 6, 5, 9, 2, 1, 7, 5, 7, 7, 5, 8, 7, 3, 4, 2, 3, 1, 5, 8, 1, 2, 5, 2, 9, 1, 6, 7, 0, 3, 9, 4, 7, 1, 7, 7, 1, 6, 0, 4, 1, 5, 3, 6, 7, 7, 5, 8, 0, 5, 7, 8, 6, 8, 7, 9, 6, 3, 9, 2, 3, 9
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OFFSET
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1,2
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.2.2 Cubic Variations of the Golden Mean, p. 9.
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LINKS
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FORMULA
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psi(1)=1, psi(n) = (1+psi(n-1))^(1/3),
lim_(n -> infinity) (psi0-psi(n))*(3*(1+1/psi0))^n, where psi0 = A060006 = the Plastic constant.
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EXAMPLE
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1.8168834242447403124481882022248074529659217577587342315812529167...
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MATHEMATICA
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digits = 99; n0 = 10; dn = 10; psi0 = A060006 = Root[x^3 - x - 1, x, 1] // N[#, 3*digits]&; Clear[psi, limPsi]; psi[1] = 1; psi[n_] := psi[n] = (1 + psi[n - 1])^(1/3) // N[#, 3*digits]&; limPsi[n_] := limPsi[n] = (psi0 - psi[n])*(3*(1 + 1/psi0))^n; limPsi[n = n0]; limPsi[n = n0 + dn]; While[RealDigits[limPsi[n], 10, digits] != RealDigits[limPsi[n - dn], 10, digits], Print["n = ", n ]; n = n + dn]; RealDigits[limPsi[n], 10, digits] // First
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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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