A077601 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.

2, 9, 8, 7, 4, 5, 8, 1, 3, 6, 6, 8, 7, 2, 2, 0, 0, 7

Offset

1,1

Links

Table of n, a(n) for n=1..18.

Example

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...

Mathematica

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 *)

Crossrefs

Cf. A074586, A074587, A077596, A077598, A077599, A077600, A077602.

Sequence in context: A021081 A018799 A076219 * A090930 A346429 A258412

Adjacent sequences: A077598 A077599 A077600 * A077602 A077603 A077604

Keyword

cons,nonn,more

Author

Benoit Cloitre and Paul D. Hanna, Nov 10 2002

Status

approved