New Sequence from wrong Comment in A083088

[Rainer Rosenthal]

pauldhanna at juno.com wrote:

>> One last point: A097682 uses sqrt(2) in the Digamma-context
>> and I am a bit uneasy about this after the "near miss" in
>> A083088. Is A097682 waterproof?
>  
> You can be sure that A097682 is air-tight.  It is a proven result 
> ... to complete an infinite array of constants involving Pi, e,...
> as well as square-roots of integers ... 
> A097682 involves row 8 of this array. 

Dear Paul

Thank you for sending me the lovely paper. It may be well over
my head and so you can see how bad it is having a misleading
comment in A083088. This comment suggests a *simple* relationship
between the Digamma function and sqrt(2). And this is wrong.
I wonder that you don't get angry about such a comment.

>> As soon as my new sequence will show up in the OEIS
>> it would be nice to cancel the wrong comment in A083088.
>> This would be best done by Paul himself, I think.
>  
> Should the comment be moved to your new sequence?

No, because the comment is the /definition/ of my new sequence.

This comment in A083088 says:
The greatest number of consecutive integer reciprocals,
beginning at 1/n, which may be added without exceeding 1.

As sequence A083088 starts with n=0, this is at least
sloppy and should read 1/(n+1) instead of 1/n.
Then there is A083088(24) = 41, but you can add 42
consecutive integer reciprocals beginning at 1/25 without
exceeding 1.

I already proposed a comment, mentioning A083088 and the
"near miss". It would be nice to know if this isn't 
just coincidence but has some asymptotic basis, given by
e.g. your other sequence A097682. Please forgive me that I became
suspicious after the blunder in A083088 (which is not your
fault!).

Many thanks to Robert Israel who immediately "declumsied" my
Maple code.

Cheers,
Rainer Rosenthal
r.rosenthal at web.de