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

Author

Jean-François Alcover, Aug 06 2014

Keywords

• nonn
• cons

Examples

			1.8168834242447403124481882022248074529659217577587342315812529167...
		

References

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

Links

• Steven R. Finch, Errata and Addenda to Mathematical Constants
• Eric Weisstein's World of Mathematics, Plastic Constant
• Wikipedia, Plastic number

Crossrefs

Cf. A060006.

Programs

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

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.