Farey Sequence implemenatationI'm trying to use the Farey sequence to get the next lowest reduced fraction in a list. For example, for n = 8, we have … , 1 3 , 3 8 , 2 5 , 3 7 , 1 2 , …So let's take 3 8 and 2 5 and attempt to get 3 7 . p = ⌊ n + b d ⌋ c − a q = ⌊ n + b d ⌋ d − b a = 3 , b = 8 , c = 2 , d = 5 , n = 8 p = [ 8 + 8 5 ] ⋅ 2 − 3 q = [ 8 + 8 5 ] ⋅ 5 − 8 p q = 3.4 8 ≠ 3 7 Am I using the equation wrong?

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Farey Sequence implemenatationI&#039;m trying to use the Farey sequence to get the next lowest reduced fraction in a list. For example, for   n  =  8, we have   …  ,      1    3    ,      3    8    ,      2    5    ,      3    7    ,      1    2    ,  …So let&#039;s take       3    8   and       2    5   and attempt to get       3    7  .  p  =      ⌊                            n          +          b                d              ⌋    c  −  a  q  =      ⌊                            n          +          b                d              ⌋    d  −  b  a  =  3  ,  b  =  8  ,  c  =  2  ,  d  =  5  ,  n  =  8  p  =  [            8      +      8        5    ]  ⋅  2  −  3  q  =  [            8      +      8        5    ]  ⋅  5  −  8      p    q    =      3.4    8    ≠      3    7  Am I using the equation wrong?

exhumatql · Accepted Answer

Well, according to your equations, you have to take the floor of             n      +      b        d  . In your example, it&#039;s       ⌊                  8        +        8            5        ⌋    =  3. Your p is then   (  3  ⋅  2  )  −  3  =  3, and your q is    (  3  ⋅  5  )  −  8  =  7

Farey Sequence implemenatation I'm trying to use the Farey sequence to get the next lowest reduced

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