PS re 2-surprising seqs

[N. J. A. Sloane]

Here is the definition:

Fix the number, A, of different letters that you can use

A 2-surprising sequence is a finite string of letters
such that for each pair of letters X and Y (possibly equal)
and each distance d, there is at most one position
where X precedes Y by distance d

For A = 2, if the letters are x and y, then

xxy and xxyx are 2-surprising, but xxyy is not

because x-y- and -x-y both have d=2



3-surprising:  for any triplet of symbols X, Y, Z,
and any two distance d1, d2
there is at most one palce where we see 
X (d1) Y (d2) Z