A112330 a(n) is the number of terms in the n-th row of A106394.

1, 2, 3, 3, 4, 5, 6, 5, 7, 8, 7, 6, 9, 7, 8, 8, 9, 8, 8, 9, 8, 11, 11, 11, 11, 9, 14, 10, 15, 12, 12, 15, 11, 14, 10, 14, 12, 13, 12, 16, 15, 13, 12, 12, 17, 13, 16, 16, 15, 16, 19, 14, 17, 16, 16, 21, 15, 18, 16, 18, 18, 18, 19, 21, 20, 19, 20, 22, 17, 20, 27, 19, 25, 20, 18, 23, 24

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..142

Example

H(4) = 1 + 1/2 + 1/3 + 1/4 = 25/12 has the Egyptian fraction expansion, by the greedy algorithm, of 1 + 1 + 1/12. Since there are 3 terms in this expansion, a(4) = 3.

Mathematica

egyptFraction[f_] := Ceiling[1/Most[NestWhileList[# - 1/Ceiling[1/#] &, f, # != 0 &]]]; a[n_] := Length[egyptFraction[HarmonicNumber[n]]]; Array[a, 100] (* Amiram Eldar, Apr 09 2022 *)

Crossrefs

Cf. A001008, A002805, A105401, A106394, A106395.

Sequence in context: A094182 A300587 A075699 * A332682 A304183 A157222

Adjacent sequences: A112327 A112328 A112329 * A112331 A112332 A112333

Keyword

nonn

Author

Leroy Quet, Sep 04 2005

Extensions

More terms from David Wasserman, Apr 16 2009

Status

approved