OFFSET
0,1
EXAMPLE
0.91052326250854940299766172467999718134715243829709...
MATHEMATICA
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 *)
x1 = N[Table[h[a[t]] - h[a[t - 1]], {t, 2, z, 50}], 50]
Last[RealDigits[x1, 10]] (* A227817 *)
x2 = N[Table[a[n]/a[n - 1], {n, 2, z, 50}], 50] (* A227818 *)
Last[RealDigits[x2, 10]] (* A227818 *)
(* Peter J. C. Moses, Jul 23 2013 *)
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Jul 31 2013
STATUS
approved