A227817 - OEIS

%I #19 May 22 2021 04:26:51

%S 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,

%T 8,1,3,4,7,1,5,2,4,3,8,2,9,7,0,9

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

%e 0.91052326250854940299766172467999718134715243829709...

%t 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 *)

%t x1 = N[Table[h[a[t]] - h[a[t - 1]], {t, 2, z, 50}], 50]

%t Last[RealDigits[x1, 10]]  (* A227817 *)

%t x2 = N[Table[a[n]/a[n - 1], {n, 2, z, 50}], 50]  (* A227818 *)

%t Last[RealDigits[x2, 10]]   (* A227818 *)

%t (* _Peter J. C. Moses_, Jul 23 2013 *)

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

%Y Cf. A227816, A227818.

%K nonn,cons,more

%O 0,1

%A _Clark Kimberling_, Jul 31 2013