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<code>foldi</code> is on [[Fold#Tree-like_folds|Tree-like folds]] page. <code>union</code> and more at [[Prime numbers#Sieve_of_Eratosthenes|Prime numbers]].
 
<code>foldi</code> is on [[Fold#Tree-like_folds|Tree-like folds]] page. <code>union</code> and more at [[Prime numbers#Sieve_of_Eratosthenes|Prime numbers]].
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Also, the math formula for Sieve of Eratosthenes,
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::::<math>\textstyle\mathbb{S} = \mathbb{N}_{2} \setminus \bigcup_{p\in \mathbb{S}} \{n p:n \in \mathbb{N}_{p}\}</math>
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where
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::::<math>\textstyle\mathbb{N}_{k} = \{ n \in \mathbb{N} : n \geq k \}</math> &emsp; . . . or, &ensp;<math>\textstyle\mathbb{N}_{k} = \{k\} \bigcup \mathbb{N}_{k+1}</math> &emsp; :)&emsp;:) .
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Trial division sieve:
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::::<math>\textstyle\mathbb{T} = \{n \in \mathbb{N}_{2}: (\not\exists p \in \mathbb{T}) (p\leq \sqrt{n} \and p\mid n)\}</math>

Revision as of 09:43, 29 August 2011

I'm interested in Haskell.

I like this:

--   inifinte folding idea due to Richard Bird
--   double staged production idea due to Melissa O'Neill
--   tree folding idea Dave Bayer / simplified formulation Will Ness
primes = 2 : g (fix g) 
  where                
    g ps = 3 : gaps 5 (foldi (\(q:qs) -> (q:) . union qs) 
                             [[p*p, p*p+2*p..] | p <- ps])
    gaps k s@(c:t)                
       | k < c = k : gaps (k+2) s     -- | k<=c = minus [k,k+2..] s
       | True  =     gaps (k+2) t     --   fused to avoid a space leak
 
fix g = xs where xs = g xs            -- global defn to avoid space leak

foldi is on Tree-like folds page. union and more at Prime numbers.

Also, the math formula for Sieve of Eratosthenes,

\textstyle\mathbb{S} = \mathbb{N}_{2} \setminus \bigcup_{p\in \mathbb{S}} \{n p:n \in \mathbb{N}_{p}\}

where

\textstyle\mathbb{N}_{k} = \{ n \in \mathbb{N} : n \geq k \}   . . . or,  \textstyle\mathbb{N}_{k} = \{k\} \bigcup \mathbb{N}_{k+1}   :) :) .

Trial division sieve:

\textstyle\mathbb{T} = \{n \in \mathbb{N}_{2}: (\not\exists p \in \mathbb{T}) (p\leq \sqrt{n} \and p\mid n)\}