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

%I A240982 #14 Feb 16 2025 08:33:21
%S A240982 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,
%T A240982 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,
%U A240982 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
%N A240982 Decimal expansion of the limit of a recursive sequence connected to the Plastic constant (A060006).
%D A240982 Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.2.2 Cubic Variations of the Golden Mean, p. 9.
%H A240982 Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>
%H A240982 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PlasticConstant.html">Plastic Constant</a>
%H A240982 Wikipedia, <a href="http://en.wikipedia.org/wiki/Plastic_number">Plastic number</a>
%F A240982 psi(1)=1, psi(n) = (1+psi(n-1))^(1/3),
%F A240982 lim_(n -> infinity) (psi0-psi(n))*(3*(1+1/psi0))^n, where psi0 = A060006 = the Plastic constant.
%e A240982 1.8168834242447403124481882022248074529659217577587342315812529167...
%t A240982 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
%Y A240982 Cf. A060006.
%K A240982 nonn,cons
%O A240982 1,2
%A A240982 _Jean-François Alcover_, Aug 06 2014