Corrections wanted to extend sequence A035335

[Richard Mathar]

Could someone please calculate more terms of this sequence? I wonder if it is already in the EIS. (I may have made a mistake with my terms.)

Each a(n) is the (+ or -) integer, given the earlier terms of the sequence, such that sum{k=1 to n} a(k)/k is the best approximation to the natural log of n.

In other words, a(n) = the nearest integer to
n*(ln(n) - sum{k=1 to n-1} a(k)/k).

I get that the sequence begins:

0,1,2,1,1,1,1,1,1,1,1,2,

When, if ever, does the sequence become negative?

Thanks,
Leroy Quet