A240982 Decimal expansion of the limit of a recursive sequence connected to the Plastic constant (A060006).

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

Offset

1,2

References

Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.2.2 Cubic Variations of the Golden Mean, p. 9.

Links

Table of n, a(n) for n=1..99.

Steven R. Finch, Errata and Addenda to Mathematical Constants

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: A157697 A388709 A281785 * A258146 A182551 A388132

Adjacent sequences: A240979 A240980 A240981 * A240983 A240984 A240985

Keyword

nonn,cons

Author

Jean-François Alcover, Aug 06 2014

Status

approved