Re: [Haskell-cafe] Is there an efficient way to generate Euler's totient function for [2, 3..n]?

2011-05-22 Thread Henning Thielemann
Daniel Fischer schrieb: On Saturday 14 May 2011 19:38:03, KC wrote: Instead of finding the totient of one number, is there a quicker way when processing a sequence? For some sequences. You may find alternative ways of computation in the Online Encyclopedia of Integer Sequences.

Re: [Haskell-cafe] Is there an efficient way to generate Euler's totient function for [2, 3..n]?

2011-05-22 Thread KC
It's declarative and may help to verify more efficient implementations. WOW! Good insight. :) On Sun, May 22, 2011 at 9:27 AM, Henning Thielemann schlepp...@henning-thielemann.de wrote: Daniel Fischer schrieb: On Saturday 14 May 2011 19:38:03, KC wrote: Instead of finding the totient of

[Haskell-cafe] Is there an efficient way to generate Euler's totient function for [2, 3..n]?

2011-05-14 Thread KC
Is there an efficient way to generate Euler's totient function for [2,3..n]? Or an arithmetical sequence? Or a geometric sequence? Or some generalized sequence? -- -- Regards, KC ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org

Re: [Haskell-cafe] Is there an efficient way to generate Euler's totient function for [2, 3..n]?

2011-05-14 Thread Warren Henning
On Sat, May 14, 2011 at 10:22 AM, KC kc1...@gmail.com wrote: Is there an efficient way to generate Euler's totient function for [2,3..n]? Or an arithmetical sequence? Or a geometric sequence? Or some generalized sequence? Does computing the totient function require obtaining the prime

Re: [Haskell-cafe] Is there an efficient way to generate Euler's totient function for [2, 3..n]?

2011-05-14 Thread KC
Instead of finding the totient of one number, is there a quicker way when processing a sequence? -- From: http://www.haskell.org/haskellwiki/99_questions/Solutions/34 totient :: Int - Int totient n = length [x | x - [1..n], coprime x n] where coprime a b = gcd a b == 1 On Sat, May 14,

Re: [Haskell-cafe] Is there an efficient way to generate Euler's totient function for [2, 3..n]?

2011-05-14 Thread Daniel Fischer
On Saturday 14 May 2011 19:38:03, KC wrote: Instead of finding the totient of one number, is there a quicker way when processing a sequence? For some sequences. For [1 .. n] (you asked about [2 .. n], but it may be better to include 1), it can efficiently be done, O(n*log log n), iirc.