# [seqfan] Re: Another surprising omission from OEIS

Maximilian Hasler maximilian.hasler at gmail.com
Fri Nov 13 16:19:53 CET 2009

```Dear Seqfans (& author of A167389 if on the list),

I apologize for the style of my last message.
I did not want to be insulting, and I should not have used the term
"complete nonsense", which in some sense is nonsense in itself.

Actually I intended to reply to the author of the O.P. in private.

In case the author of the sequence is on this list,
I would like to ask him to add the clarification of what is W(n,x),
which is not mentioned in any of the submitted links.

(I do understand that this refers to the choice of the branch of the W
function when extended to the complex numbers.)

Also, I would like to ask him to make some elementary simplifications
e.g. exp(-ln(2)+...) =  exp(...)/2
or to explain why he does not do it.

Also, it would be nice to say if / why this is an integer sequence, or
if it is missing a "round()" in the definition. (This might clarify a
lot of things.)

Then it would also be nice to know what is meant by  "argument".
As far as I can understand, the argument of a complex number is either
a value in a fixed, half-open interval of length 2*pi, or the
equivalence class of all such values, i.e. an element of R / (2 pi Z).
At best, it could also stand for an arbitrary representative of such a
class, in which case the sequence would not be well defined.

That said, I hope I did not spoil this nice Friday 13th to you, with
my compulsive posting.

Maximilian
PS: first differences of the missing numbers in the sequence are :
3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 4, 3,
3, 3, 4, 3, 3, 3, 4,...
Notice that there is an occurrence of  "4, 3, 3, 4".

On Fri, Nov 13, 2009 at 10:10 AM, Maximilian Hasler
<maximilian.hasler at gmail.com> wrote:
>> in some vague sense from 3 to 1).  A167389 is a real example of this:
>> though not base-dependent, it seems to be an entirely arbitrary
>> function
>> (argument(exp(-(ln(2)+W(n,-(1/2)*ln(2)))/ln(2)))*ln(2)+Im(W(n,-(1/2)*ln(2))))/(2*Pi*ln(2))
>
> anyway, if I see
>
> (..(exp(-ln(2)+...)/ln(2)))*ln(2)+...
>
> then I already have some prejudice...
>
> "argument(...)/2pi"  does not improve anything ...
>
> IMO that's complete nonsense, but of course I might be wrong...
>
> Whatsoever, I think it is insulting to "submit" such a thing and let
> tens or hundreds of people try their best in making a sense of it.
>
> Maximilian
>

```