Ken Tilton wrote:

> > Say I want to create a function that fills a list of length n with a
> > sequence that counts from 1 to n, at a given interval r and returns
> > the list. And this process being generalized for any given length or
> > interval. Of course the length and interval have to be relatively
> > prime.
> >
> > For example: If the interval is 3 and the length is 17, the list
> > returned would be...
> > (1 7 13 2 8 14 3 9 15 4 10 16 5 11 17 6 12)
> > You can see that, since the interval is 3, if you read every 3 in the
> > final list you will see 1 2 3 4...etc.
> >
> > I have done this several different ways, but ran into some
> > limitations, and am now back to work on a better way. Any
> > suggestions? I have a feeling it is much simpler than I am making it.
>
> Maybe?:
>
> (let ((n 17)(i 3))
> (loop with a = (make-array n)
> for x below n
> do (setf (svref a (mod (* i x) n)) (1+ x))
> finally (return (coerce a 'list))))
Gauche Scheme:

(define (foo top interval)
(define len (ceiling (/ top interval)))
(take
(apply append-map list
(map (lambda (i) (iota len (+ 1 (* i len)))) (iota interval)))
top))

(foo 17 3)
===>
(1 7 13 2 8 14 3 9 15 4 10 16 5 11 17 6 12)

(foo 18 3)
===>
(1 7 13 2 8 14 3 9 15 4 10 16 5 11 17 6 12 18)