A227818 Decimal expansion of limit of c(n)/c(n-1), where c = A227816.

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, 2, 3, 0, 7, 0, 6, 0, 0, 5, 5, 7, 5, 0, 1, 5, 7

Offset

1,1

Links

Table of n, a(n) for n=1..50.

Example

2.4856228263933033216124061911869342307060055750157...

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

Cf. A227816, A227817.

Sequence in context: A092892 A146079 A165669 * A300890 A021893 A036117

Adjacent sequences: A227815 A227816 A227817 * A227819 A227820 A227821

Keyword

nonn,cons,more

Author

Clark Kimberling, Jul 31 2013

Status

approved