Re A little fun with Fibonacci, tau,

[N. J. A. Sloane]

Thomas B. said:

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.

(end quote)


Me:  Probably what is going on here is the "Beatty effect".
If a and b are irrational nos with 1/a + 1/b = 1
then [na] and [nb] are complementary seqs.

NJAS