A125097.gif: (Very) nice patterns

[N. J. A. Sloane]

The other day Zak said:
> Neil,
> seqfans,
>
> 1. Have a look at this full graph -
> aint these patterns (very) nice?!
> It may be known, but still it's nice...
>
> 2. Is it possible to
> put "the extended graph" into OEIS?
> In the standard graph no patterns are seen at all...
>
> 3. Neil removed  keyword "nice" from A125097
> (as he did regularly with ny sequences)-
> as if I insist that it's me who is "nice"
> not it is the seq which is nice.
>

Here is my reply:
1. i will use the b-file
2. we don't need the gif since the graph button will use the b-file
3. the definition of the sequence is
     a(n) is k such that k*(2n+1) mod 1000 = 123, or 2n+1 if no such k exists.
Now there is rule that a sequence should not depend on an arbitrary 
parameter. Here we have two of them. Why not:
a(n) is k such that k*(2n+1) mod 44445555 = 321345, or 2n+1 if no such k exists. ?
4. the sequence is not finite (a(1000) = 123)
5. although i know you are a nice guy, i do not think this sequence is nice.
Best regards
Neil