How can I generate the Rowland prime sequence idiomatically in J?
- by Gregory Higley
If you're not familiar with the Rowland prime sequence, you can find out about it here. I've created an ugly, procedural monadic verb in J to generate the first n terms in this sequence, as follows:
rowland =: monad define
result =. 0 $ 0
t =. 1 $ 7
while. (# result) < y do.
a =. {: t
n =. 1 + # t
t =. t , a + n +. a
d =. | -/ _2 {. t
if. d > 1 do.
result =. ~. result , d
end.
end.
result
)
This works perfectly, and it indeed generates the first n terms in the sequence. (By n terms, I mean the first n distinct primes.)
Here is the output of rowland 20:
5 3 11 23 47 101 7 13 233 467 941 1889 3779 7559 15131 53 30323 60647 121403 242807
My question is, how can I write this in more idiomatic J? I don't have a clue, although I did write the following function to find the differences between each successive number in a list of numbers, which is one of the required steps. Here it is, although it too could probably be refactored by a more experienced J programmer than I:
diffs =: monad : '}: (|@({.-2&{.) , $:@}.) ^: (1 < #) y'
