The Ehrenfeucht-Mycielski Sequence

This sequence of binary digits was introduced by A. Ehrenfeucht and J. Mycielski in A psuedo-random sequence: how random is it?, Amer. Math. Monthly, 99 (1992), 373-375. The sequence starts 010 and continues according to the following rule: find the longest sequence at the end that has occurred at least once previously. If there are more than one previous occurrences select the last one. The next digit of the sequence is the opposite of the one following the previous occurrence. Thus, the sequence begins 010011010111000100001111011...

An unpublished manuscript I have written about this and related sequences entitled Laws of large numbers for some non-repetitive sequences is available in either postscript or tex source form.

Files containing varying numbers of terms of the sequence are available below for experimentation. (The files, after any necessary uncompression, contain only binary digits and newlines every 80 characters):