A112286 a(n) = numerator of sum of reciprocals of the terms of the continued fraction for H(n) = Sum_{k=1..n} 1/k.

1, 3, 11, 7, 71, 7, 17, 152, 2699, 701, 691, 248, 133, 137, 61933, 809, 20705, 64896, 3587, 17449, 445, 61897, 208, 20663, 1163, 982, 27281, 1871, 2466139, 44339, 21293609, 13417971, 6229, 54238033, 99737, 3585191, 33583, 40756259, 5956441

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Harmonic Number

Eric Weisstein's World of Mathematics, Continued Fraction

Example

1 +1/2 +1/3 +1/4 +1/5 +1/6 = 49/20 = 2 + 1/(2 + 1/(4 + 1/2)).
So a(6) is 7, the numerator of 7/4 = 1/2 + 1/2 + 1/4 + 1/2.

Mathematica

f[n_] := Plus @@ (1/# &) /@ ContinuedFraction[Sum[1/k, {k, n}]]; Table[Numerator[f[n]], {n, 40}] (* Ray Chandler, Sep 06 2005 * )

Crossrefs

m-th harmonic number H(m) = A001008(m)/A002805(m).

Cf. A055573, A058027, A100398, A110020, A112287.

Sequence in context: A322364 A250034 A006495 * A126261 A050097 A330566

Adjacent sequences: A112283 A112284 A112285 * A112287 A112288 A112289

Keyword

nonn,frac

Author

Leroy Quet, Sep 01 2005

Extensions

Extended by Hans Havermann and Ray Chandler, Sep 06 2005

Status

approved