A227817 Decimal expansion of limit of H(c(n)) - H(c(n-1)), where c = A227816 and H = harmonic number.

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

Offset

0,1

Links

Table of n, a(n) for n=0..49.

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

Cf. A001008, A002805 (numerator and denominator of harmonic numbers).

Cf. A227816, A227818.

Sequence in context: A273636 A248414 A176980 * A372948 A102209 A222131

Adjacent sequences: A227814 A227815 A227816 * A227818 A227819 A227820

Keyword

nonn,cons,more

Author

Clark Kimberling, Jul 31 2013

Status

approved