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%I #13 Nov 16 2023 10:04:04
%S 2,9,8,7,4,5,8,1,3,6,6,8,7,2,2,0,0,7
%N Decimal expansion of the limit of the maximum real root of M(n,-x) as n -> infinity, where M(n,x) is the n-th Moebius polynomial and satisfies M(n,-1) = mu(n) the Moebius function of n.
%e Let R(n) = max zero of M(n,-x), then R(5) = 2.961148315..., R(10)= 2.980078049..., R(15)= 2.986397371..., R(oo)= 2.98745813668722007...
%t digits = 18; t[n_, 1] = 1; t[n_, k_] := t[n, k] = Sum[ Floor[n/m]*t[m, k-1], {m, 1, n-1}]; m[n_, x_] := Sum[ t[n, k+1]*x^k, {k, 0, n}]; Clear[f]; f[n_] := f[n] = Table[ Root[ m[n, -x], k, x], {k, 1, n-1}] // N[#, digits+5]& // Re // Max; Catch[ For[ n = 3, True, n++, If[ RealDigits[ f[n]][[1]][[1 ;; digits+2]] == RealDigits[ f[n-1]][[1]][[1 ;; digits+2]], Throw[f[n]]]]] // RealDigits[#, 10, digits+1]& // First (* _Jean-François Alcover_, Apr 12 2013 *)
%Y Cf. A074586, A074587, A077596, A077598, A077599, A077600, A077602.
%K cons,nonn,more
%O 1,1
%A _Benoit Cloitre_ and _Paul D. Hanna_, Nov 10 2002
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