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
Examples
0.91052326250854940299766172467999718134715243829709...
Crossrefs
Programs
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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 *)