A little fun with Fibonacci, tau, etc.

[Thomas Baruchel]

Hi,

I noticed (thanks to the software eisseeker) that sequences
A057843 and A007064 were very similar; here is the beginning of both

%V A057843 -1,2,4,7,10,12,15,17,20,23,25,28,31,33,36,38,41,44,46,49,51,54,57,59,
%S A007064 1,4,7,9,12,14,17,20,22,25,27,30,33,35,38,41,43,46,48,51,

As you can see, if you "realign" both sequences by making "4" match in
both sequences, you may find more than one third of terms belonging to both
sequences at the exact position.
Definitions are:

%N A057843 floor(n*tau^2) - 3, tau = (1+sqrt(5))/2.
%Y A057843 Subtract 2 from each term of A003622. Complement of A058065.

and

%N A007064 Numbers not of form "nearest integer to n*tau", tau=(1+sqrt(5))/2.
%C A007064 First column of Stolarsky array.

Now, I had the idea building the sequence of positions of terms
differing, in this way:
"take A007064, consider initial offset is 1, and then look if
A007064(n) = A057843(n+1) or not; in case they are different, take n
in the new sequence".

It makes:
1 4 6 9 11 12 14 17 19 22 25 27 30 32 33 35 38 40 43 46 48 51
Of course, I looked in the database if it belongs to it, and I found
a very close sequence:
(monospace font is recommanded)

mine is:     1 4 6 9 11 12 14 17 19 22 25 27 30 32 33 35 38 40 43 46 48 51
and A003259: 1,4,6,9,11,   14,17,19,22,25,27,30,32,   35,38,40,43,45,48,51
                         !                          !              !

but I don't understand what is exactly A003259. Can someone help ?

Should I again build the sequence of positions of terms differing?
(here: 6, 15, 20 ;-)

Is there here something worth a comment in the database ?
(closeness of A057843 and A007064, or closeness of my sequence and A003259 ?)

Regards,