Math Is Fun Forum

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Non-repeating sequences

(This maybe isn't the right place to post this, since I'm only asking out of curiosity, but it seemed most appropriate. Nothing urgent though.)

I'm looking for sequences with the property that it's impossible to find a string of number(s) that directly follows itself.

eg.
11
1223
1212
123123

all won't work.

I'm trying to find the maximum length of that kind of sequence, where all its elements are taken from the first n integers.

The first two cases are easy:

n=1:
1

n=2:
121

But with n=3 it gets quite a lot harder.

First I thought I saw a pattern and went with 1213121 as the best one.
But in fact, that can be improved by 12131231321, for example, and that's very beatable as well.

Can anyone find the limit (if there is one)?

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Why did the vector cross the road?
It wanted to be normal.