Sequences given by modulated Sturmian functions: Difference between revisions
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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 | 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]\displaystyle{ f(2^a 3^b 5^c 7^d) = \theta(a+b+2c) (-1)^{b+c+d} }[/math]
where [math]\displaystyle{ \theta(n) }[/math] is [math]\displaystyle{ 1 }[/math] if [math]\displaystyle{ \lfloor (n+1) \frac{\sqrt{5}-1}{2} \rfloor = \lfloor n \frac{\sqrt{5}-1}{2} \rfloor }[/math] and [math]\displaystyle{ -1 }[/math] otherwise.
+-++----++++-+--+-++-+-+--+-+-++--+--++-++--++--++-+-+-+--++ ----++-++-++----+-++-++--++-+--++-++----+++-++---+++---++-+- -+--++++-+-+--++--+-+-+--++-++-+--++-+---++--++---++--+++--+ -+--++++--+-++-+---++-+---++-++-+-++-+---++--++--++-+--+--++ ++---+++--++--+-+---++--++++--+--+++-+-+----+-++++-+---++-+- +-+-++-+--++-+--+--++---+++-++---+-+--++++---++-+-++---+++-- -+--+++---+++-++--++-+-+--+--++--++--++-+--+++
