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

Author

Clark Kimberling, Jul 31 2013

Keywords

• nonn
• cons
• more

Examples

			0.91052326250854940299766172467999718134715243829709...
		

Crossrefs

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

Cf. A227816, A227818.

Programs

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 *)