Difference between revisions of "Sequences given by modulated Sturmian functions"

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(New page: This sequence, of length 406, satisfies the formula <math>f(2^a 3^b 5^c 7^d) = \theta(a+b+2c) (-1)^{b+c+d}</math> where <math>\theta(n)</math> is <math>1</math> if <math>\lfloor (n+1) \f...)
 
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This sequence, of length 406, satisfies the formula
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This discrepancy-2 sequence of length 406 satisfies the formula
  
 
<math>f(2^a 3^b 5^c 7^d) = \theta(a+b+2c) (-1)^{b+c+d}</math>
 
<math>f(2^a 3^b 5^c 7^d) = \theta(a+b+2c) (-1)^{b+c+d}</math>

Revision as of 06:15, 20 January 2010

This discrepancy-2 sequence of length 406 satisfies the formula

[math]f(2^a 3^b 5^c 7^d) = \theta(a+b+2c) (-1)^{b+c+d}[/math]

where [math]\theta(n)[/math] is [math]1[/math] if [math]\lfloor (n+1) \frac{\sqrt{5}-1}{2} \rfloor = \lfloor n \frac{\sqrt{5}-1}{2} \rfloor[/math] and [math]-1[/math] otherwise.

+-++----++++-+--+-++-+-+--+-+-++--+--++-++--++--++-+-+-+--++
----++-++-++----+-++-++--++-+--++-++----+++-++---+++---++-+-
-+--++++-+-+--++--+-+-+--++-++-+--++-+---++--++---++--+++--+
-+--++++--+-++-+---++-+---++-++-+-++-+---++--++--++-+--+--++
++---+++--++--+-+---++--++++--+--+++-+-+----+-++++-+---++-+-
+-+-++-+--++-+--+--++---+++-++---+-+--++++---++-+-++---+++--
-+--+++---+++-++--++-+-+--+--++--++--++-+--+++