Difference between revisions of "User:WillNess"
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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> |
::::<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 |
where |
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::::<math>\textstyle\mathbb{N}_{k} = \{ n \in \mathbb{N} : n \geq k \}</math>   . . . or,  <math>\textstyle\mathbb{N}_{k} = \{k\} \bigcup \mathbb{N}_{k+1}</math>   :) :) . |
::::<math>\textstyle\mathbb{N}_{k} = \{ n \in \mathbb{N} : n \geq k \}</math>   . . . or,  <math>\textstyle\mathbb{N}_{k} = \{k\} \bigcup \mathbb{N}_{k+1}</math>   :) :) . |
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Trial division sieve: |
Trial division sieve: |
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− | ::::<math>\textstyle\mathbb{T} = \{n \in \mathbb{N}_{2}: (\ |
+ | ::::<math>\textstyle\mathbb{T} = \{n \in \mathbb{N}_{2}: (\forall p \in \mathbb{T})(2\leq p\leq \sqrt{n}\, \Rightarrow \neg{(p \mid n)})\}</math> |
If you're put off by self-referentiality, just replace <math>\mathbb{S}</math> or <math>\mathbb{T}</math> on the right-hand side of equations with <math>\mathbb{N}_{2}</math>. |
If you're put off by self-referentiality, just replace <math>\mathbb{S}</math> or <math>\mathbb{T}</math> on the right-hand side of equations with <math>\mathbb{N}_{2}</math>. |
Revision as of 18:42, 5 September 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 xs = 3 : gaps 5 (foldi (\(c:cs) -> (c:) . union cs)
[[x*x, x*x+2*x..] | x <- xs])
gaps k s@(c:t)
| k < c = k : gaps (k+2) s -- minus [k,k+2..] (c:t), k<=c
| 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.
The math formula for Sieve of Eratosthenes,
where
- . . . or, :) :) .
Trial division sieve:
If you're put off by self-referentiality, just replace or on the right-hand side of equations with .