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%I #19 May 22 2021 04:26:42
%S 2,4,8,5,6,2,2,8,2,6,3,9,3,3,0,3,3,2,1,6,1,2,4,0,6,1,9,1,1,8,6,9,3,4,
%T 2,3,0,7,0,6,0,0,5,5,7,5,0,1,5,7
%N Decimal expansion of limit of c(n)/c(n-1), where c = A227816.
%e 2.4856228263933033216124061911869342307060055750157...
%t z = 300; h[n_] := h[n] = HarmonicNumber[N[n, 500]]; x = 3; y = 6; a[1] = -1 + Ceiling[w /. FindRoot[h[w] == 2 h[y] - h[x - 1], {w, 1}, WorkingPrecision -> 400]]; a[2] = -1 + Ceiling[w /. FindRoot[h[w] == 2 h[a[1]] - h[y], {w, a[1]}, WorkingPrecision -> 400]]; Do[s = 0; a[t] = -1 + Ceiling[w /. FindRoot[h[w] == 2 h[a[t - 1]] - h[a[t - 2]], {w, a[t - 1]}, WorkingPrecision -> 400]], {t, 3, z}]; m = Map[a, Range[z]]; (* A227816 *)
%t x1 = N[Table[h[a[t]] - h[a[t - 1]], {t, 2, z, 50}], 50]
%t Last[RealDigits[x1, 10]] (* A227817 *)
%t x2 = N[Table[a[n]/a[n - 1], {n, 2, z, 50}], 50] (* A227818 *)
%t Last[RealDigits[x2, 10]] (* A227818 *)
%t (* _Peter J. C. Moses_, Jul 23 2013 *)
%Y Cf. A227816, A227817.
%K nonn,cons,more
%O 1,1
%A _Clark Kimberling_, Jul 31 2013