Longest binary sequence with no equal n-length subsequences

Question

We are looking for an algorithm with the following criteria.

Input is an arbitrary positive integer (n), that represents the length of the compare subse

Answer 1

Using the free Minizinc constraint solver, you can write the search for a given sequence length as follows:

int: n = 3;
int: k = pow(2,n)+n-1;

array[1..k] of var 0..1: a;

constraint
  forall (i in 1..k-n) (
    forall (j in i+1..k-n+1) (
      exists (x in 0..n-1)(
        a[i+x] != a[j+x]
      )
    )
  );

solve satisfy;

output [show(a[m]) | m in 1..k];

For n=3, the longest sequence is

1110100011

k=11 yields UNSATISFIABLE

It took 71ms to find the sequence on k=10 bits for sub-sequence length n=3. For sub-sequence length n=9, the total sequence of 520 bits was found in 6.1s.