Thanks Dan. Yes, I like the idea of using OEIS for getting suggestions on the sequences.
Regards, Yuva On Fri, Jan 15, 2010 at 12:09 PM, Dan Bron <[email protected]> wrote: > Yuvaraj Raghuvir wrote: > > 1) For the J pattern I have found, is there a way to use ^: or $: forms? > > 2) Based on the math behind the Java Code, is there a different way to > > achieve this result? I am not able to formulate the problem so I did it > the > > debugging way. > > If this is the kind of output you want: > > t4 i.2 > > 0 1 1 2 1 2 2 3 1 2 2 3 2 3 3 4 > > and you wanted to use ^: then you could say something like: > > t =: >: (, >:)@:]^:[ 0: > > or, more directly: > > t =: +/"1...@#:@:i.@:(2 ^ >:) > > for example: > > t 2 > 0 1 1 2 1 2 2 3 > t 3 > 0 1 1 2 1 2 2 3 1 2 2 3 2 3 3 4 > t 4 > 0 1 1 2 1 2 2 3 1 2 2 3 2 3 3 4 1 2 2 3 2 3 3 4 2 3 3 4 3 4 4 5 > > But I'm not sure this is what you're asking for, because I haven't read the > Java or J code yet - I just took the last line of your > message as the desired output. And I'm no mathematician, but when I > encounter an interesting integer sequence I turn to OEIS for > insight. > > For example, in this case, I copied your longest sequence (quoted above), > inserted a comma between each number, and pasted it into > the search box at the top of > http://www.research.att.com/~njas/sequences/ and was directed to > A000120: > http://www.research.att.com/~njas/sequences/A000120 > > That sequence is entitled "number of 1's in binary expansion of n", which I > mechanically translated to J to produce the 2nd version, > above. A little further down the page, we read: > > To construct the sequence, start with 0 and use the rule: If k>=0 > and a(0),a(1),...,a(2^k-1) > are the 2^k first terms, then the next 2^k terms are > a(0)+1,a(1)+1,...,a(2^k-1)+1. > - Benoit Cloitre, Jan 30 2003 > > which is how I derived the first (^: based) version. So you see I didn't > have to read the code or understand its math (and > refactor) to reproduce its results. A $: based version would be pretty > easy, and is left as an exercise for those want to learn > to use OEIS. > > -Dan > > PS: Incidentally, it took me much longer to write this message than it did > to write the J code after reading the OEIS entry (the > time for that was de minimus). > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
