Multiplicative sequences
From Polymath Wiki
Any completely-multiplicative sequence of length [math]\displaystyle{ 247 }[/math] has discrepancy more than [math]\displaystyle{ 2 }[/math]. There are 500 sequences of length [math]\displaystyle{ 246 }[/math] with discrepancy [math]\displaystyle{ 2 }[/math], all of which agree at primes up to and including [math]\displaystyle{ 67 }[/math]. Here is one example:
0 + - - + - + - - + + + - - + + + - - + - + - - + + + - - + - + - - + + + - - + + - - - + - + - - + - + - + + - + - - + + + - - + + + - - + - - - + + - + - - + - + + - + + + - - - + + - - + - + - - + + - - + + - - + - + + + - - + + + - - + - + - + + - + - - + - + - - + + + - - - + + + - + - - - - + + + - - + - + + - - + + - - - + + - - + - + - + + - + - + + - + - - + + + - - + + - - - + - + - - + - + + - + + - - - + + - + + - + + - - - - + - + + + + - - - - + - + + + + - - - + + - - + - -
