Problem Statement

The Yellowstone sequence, also called the Yellowstone permutation, is defined as: For n <= 3, For n >= 4,

The sequence is a permutation of the natural numbers, and gets its name from what its authors felt was a spiking, geyser like appearance of a plot of the sequence.

a(4) is 4 because 4 is the smallest number following 1, 2, 3 in the sequence that is relatively prime to the entry before it (3), and is not relatively prime to the number two entries before it (2).

Let's start with the solution:

(load "@lib/frac.l")
(de yellow (N)
   (let (L (list 3 2 1)  I 4  C 3  D)
      (while (> N C)
         (when
            (and
               (not (idx 'D I))
               (=1 (gcd I (get L 1)))
               (> (gcd I (get L 2)) 1) )
            (push 'L I)
            (idx 'D I T)
            (setq I 4)
            (inc 'C) )
         (inc 'I) )
      (flip L) ) )
(println (yellow 30))