Multiplicative sequences: Difference between revisions
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Longest completely multiplicative sequence. |
m Note about agreement of maximal sequences. |
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Any completely-multiplicative sequence of length <math>247</math> has discrepancy more than <math>2</math>. There are 500 sequences of length <math>246</math> with discrepancy <math>2</math>. Here is one example: | Any completely-multiplicative sequence of length <math>247</math> has discrepancy more than <math>2</math>. There are 500 sequences of length <math>246</math> with discrepancy <math>2</math>, all of which agree at primes up to and including <math>67</math>. Here is one example: | ||
0 + - - + - + - - + + + - - + + + - - | 0 + - - + - + - - + + + - - + + + - - | ||
Revision as of 01:15, 13 January 2010
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 + - - + - + - - + + + - - + + + - - + - + - - + + + - - + - + - - + + + - - + + - - - + - + - - + - + - + + - + - - + + + - - + + + - - + - - - + + - + - - + - + + - + + + - - - + + - - + - + - - + + - - + + - - + - + + + - - + + + - - + - + - + + - + - - + - + - - + + + - - - + + + - + - - - - + + + - - + - + + - - + + - - - + + - - + - + - + + - + - + + - + - - + + + - - + + - - - + - + - - + - + + - + + - - - + + - + + - + + - - - - + - + + + + - - - - + - + + + + - - - + + - - + - -
