> The following are a list questions I have: > > - pi<sup>(2)</pi>(x) is non-standard, at least unusual. > Superscript usually means exponentiation. > - x should be n (I assume this is a typo) > - Square brackets sometimes mean the nearest integer. > In this case I think it just denotes grouping; the author > could have used parens.
Another item: - p_k and pi(n) are inverses of each other. In J this is made more evident by using p: and p:^:_1 to denote the two computations. ----- Original Message ----- From: Roger Hui <[EMAIL PROTECTED]> Date: Saturday, April 5, 2008 8:09 Subject: Re: [Jgeneral] How readable is J? To: General forum <[email protected]> > Well, it can not be exactly the same formula because > the J one finds semiprimes less than n while the > MathWorld one finds those less than or equal to n . > I derived the J computation before I saw the MathWorld > one and saw that they are very similar. > > As a mathematician, do you find the MathWorld formula? > > pi<sup>(2)</sup>(x)=sigma(k=1,pi(sqrt(n))) > [pi(n/p<sub>k</sub>-k+1] > > The following are a list questions I have: > > - pi<sup>(2)</pi>(x) is non-standard, at least unusual. > Superscript usually means exponentiation. > - x should be n (I assume this is a typo) > - Square brackets sometimes mean the nearest integer. > In this case I think it just denotes grouping; the author > could have used parens. > > In J, with the same reasoning, one readily derives a computation > that produces the actual semiprimes. That is an illustration > of the power of J in dealing with arrays. > > > > ----- Original Message ----- > From: John Randall <[EMAIL PROTECTED]> > Date: Saturday, April 5, 2008 6:06 > Subject: Re: [Jgeneral] How readable is J? > To: General forum <[email protected]> > > > Roger Hui wrote: > > > > > The MathWorld page doesn't give the derivation > > > > I believe the MathWorld formula is the same as the J derivation. > > > > Primes are indexed starting at 1. You iterate over primes p_k whose > > square is less than or equal to n. The term pi(n/p_k) > > counts primes q > > such that n>:(p_k)*q . You subtract (k-1) to count only primes > q with > > p_k<q . ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
