A103187 a(n) = second term in continued fraction of n-th harmonic number.

2, 1, 12, 3, 2, 1, 1, 1, 1, 50, 9, 5, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 36, 17, 11, 8, 6, 5, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 483, 71, 38, 26, 20, 16, 13, 12, 10, 9, 8, 7, 7, 6, 6, 5, 5

Offset

2,1

Links

Table of n, a(n) for n=2..99.

Formula

a(n) = floor(1/(H(n) - floor(H(n)))), where H(n) = sum{k=1 to n} 1/k.

Mathematica

f[n_] := Block[{h = HarmonicNumber[n]}, Floor[1/(h - Floor[h])]]; Table[ f[n], {n, 2, 99}] (* Robert G. Wilson v, Mar 19 2005 *)
Table[ContinuedFraction[HarmonicNumber[n]][[2]], {n, 2, 100}] (* Harvey P. Dale, May 07 2018 *)

Crossrefs

Sequence in context: A211099 A058734 A213057 * A286670 A288433 A288010

Adjacent sequences: A103184 A103185 A103186 * A103188 A103189 A103190

Keyword

nonn

Author

Leroy Quet, Mar 18 2005

Extensions

More terms from Robert G. Wilson v, Mar 19 2005

Status

approved