Output this binary sequence of length 1160:
-++-+--++-++-+--+--++-+--+--++-+--++-++-+-++--++-+---+-++-+--+--++++--+--++-+--++-++----++-++-+-++--++-+-+---++-+--++-++-+--++-+--+---+-++-+--++-++-+--+--++-++-+--++-+--+++-+-+----+++-+--+--+++---++-++-+--+--+++--+-+-+--+-+++-++-+--+--++-+--++-++-+--+--++--+++---+++-+---++-+--++--+-+--+-+++-+--++-++-+--++-+--+--++-+--++--+-++-+-+--+-+-++-+--++-+--+--++-+-+-++-+-+-++---+-+--++++--+---++-+-++-+--++-+--+--++-+--++++--+---+-++++--+--++-++-+--++-+--+--++-+--++-++-+--++-+--+--++-++-+----+++-+--++--+++---+-++-+--+-++---+-++-++-+--+--++--++++-+--+--+--++++--+--+++---++-++-+--++--+-+--+--++-++-+--+--+-+++-++-+--+--++--+-++-++-+--+--+--++-++-+--+++---++-+--++-++---+++---++-++----+++--+-++-+--+--++-+--++-++-+-++--++--++----+++-++--++----++-+++--++---+++----+-+-++-++-++-+-+----+++--++-+--++-++-+--+--+--++-+--++-++-+--++--+-+--+-+-+-++++---+-+-++--+--+-+-+-++-+-+++--+-+--+--+-+++--+-+++---++-+--+--++-++--++---++-+-++--++-+---+-++-+--+-++--++-+--++-+--+-+++-+--++--+-+-+++--+-+--++-++-+--+--+-++---+-++-+-++--++-+--+++-+----++--+-++-+-++--++-+--++-+-++--++-+---+-++-+--+++----+-+-++--++-+--++-++-++-+--+--+--++++---++---+-+-++-+-+++--+-++--+-+--+-+-++---+++-++
The sequence
This finite sequence is tightly structured in a way that I hope lends to unique methods for compression. It arises from the Erdős discrepancy problem, which was featured in a previous challenge.
Treating the terms as +1 and -1, this is a maximal-length sequence of discrepancy 2, which means that:
For every positive step size
d, if you take everyd'th term (starting with thedth term), the running sum of the resulting sequence remains between -2 and 2 inclusive.
If you think of each + to mean a step right and - to mean a step left, this means that the walk of every dth instruction never travels more than 2 steps away from the start position.
For example, for d=3, taking every 3rd term gives the sequence +-++--+--+-..., whose running sums are [1,0,1,2,1,0,1,0,-1,0,1,...], which never hit -3 or 3.
-++-+--++-++-+--+--++-+--+--++-+--+...
^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^
+ - + + - - + - - + -
1 0 1 2 1 0 1 0 -1 0 -1 ...
This sequence was found in 2014 via a computer search. See this paper, where the sequence is reproduced in Appendix B. The search proves that 1160 is the maximum length of a discrepancy-2 sequence, though there is more than one sequence of that length. The Erdős discrepancy problem, proven in 2015, says that any such sequence must have finite length for any maximum discrepancy c in place of 2.
Time requirement
Your code should finish within 5 seconds. This is to limit brute-forcing.
Output format
You can use any two fixed distinct characters or values for + and - in any list-like or string-like format. The format should be one where the 1160 bit-values can be directly read off, not for example encoded as a number via its binary representation or a string via character values. For string output, a trailing newline is allowed.
Leaderboard
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