de Bruijn like sequence
Edwin Clark
eclark at math.usf.edu
Fri Jan 9 20:13:20 CET 2004
Erik Evenson posted this sequence on sci.math today under the subject
heading "Invented New Sequence -- Any ideas for its use?"
0, 1, 2, 3, 0, 3, 1, 0, 2, 3, 2, 1, 0, 3, 1, 3, 2, 1, 2, 0, 1, 3, 1, 2, 0,
2, 3, 0, 1, 0, 2, 0, 3, 1, 2, 3, 2, 0, 1, 0, 3, 2, 1, 3, 1, 0, 3, 0, 2, 3,
1, 3, 0, 1, 2, 1, 3, 2, 0, 3, 0, 1, 3, 2, 3, 0, 2, 1, 2, 3, 1, 0, 1, 2, 0,
3, 2, 3, 1, 2, 1, 0, 2, 1, 3, 0, 3, 2, 0, 2, 1, 0, 1, 3, 0, 2
He makes the following claims (which I have verified):
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The sequence is circular; after the end it repeats again from the
beginning. The sequence is 96 digits long. The digits of the sequence is
made up of 4 different entities. For this sequence I use the digits
0,1,2,3. There are 24 of each of the 4 digits.
1) No digit is repeated in the sequence. No group of digits is repeated
in the sequence.
2) All possible four-digit combinations (taking rule #1 in account) are
represented in the forward reading of the sequence.
3) All possible four-digit combinations (taking rule #1 in account) are
represented in the BACKWARD reading of the sequence.
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It is similar to a de Bruijn sequence, but with different restrictions.
I haven't found anything like it in the OEIS or elsewhere. Perhaps someone
else has?
--Edwin
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