Next in the line of interesting sequences from The On-Line Encyclopedia of Integer Sequences is Van Eck’s sequence. Here is how it is defined:
Given the initial part of the sequence \(a_1,\ldots,a_n\) if \(a_n\) appears for the first time in the sequence, we set \(a_{n+1}\) to 0. Otherwise, we set \(a_{n+1}\) to \(n-m\) where \(a_m\) is the first time \(a_n\) appears in the sequence.
It is easier to grow lists in common lisp at the head. So, we are going to construct Van Eck’s sequence in the reverse:
(defun van-eck (xs)
(cond
((null xs) (list 0))
((not (member (car xs) (cdr xs))) (cons 0 xs))
(t (cons (1+ (position (car xs) (cdr xs))) xs))))VAN-ECKNext, we write the iterator
(defun iterate (fn init n &optional xs)
(do ((i 0 (1+ i))
(r (funcall fn init) (funcall fn r)))
((= i n) (nreverse r))))ITERATELet us test:
(iterate #'van-eck nil 50)(0 0 1 0 2 0 2 2 1 6 0 5 0 2 6 5 4 0 5 3 0 3 2 9 0 4 9 3 6 14 0 6 3 5 15 0 5 3
5 2 17 0 6 11 0 3 8 0 3 3 1)