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A240982 Decimal expansion of the limit of a recursive sequence connected to the Plastic constant (A060006). 0
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,2
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.2.2 Cubic Variations of the Golden Mean, p. 9.
LINKS
Eric Weisstein's World of Mathematics, Plastic Constant
Wikipedia, Plastic number
FORMULA
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.
EXAMPLE
1.8168834242447403124481882022248074529659217577587342315812529167...
MATHEMATICA
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
CROSSREFS
Cf. A060006.
Sequence in context: A299627 A157697 A281785 * A258146 A182551 A005486
KEYWORD
nonn,cons
AUTHOR
STATUS
approved

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)