Create Collatz sequences

collatz.clj

;; see https://www.quantamagazine.org/mathematician-terence-tao-and-the-collatz-conjecture-20191211/
;; for problem statement and definition of the sequence

(defn collatz [x]
	(if (even? x) (/ x 2) (+ (* x 3) 1)))

(defn collatz-seq [x]
	(lazy-cat [x] (collatz-seq (collatz x))))

;; test
(take 20 (collatz-seq 11))

;; user=> (take 20 (collatz-seq 11))
;; (11 34 17 52 26 13 40 20 10 5 16 8 4 2 1 4 2 1 4 2)

;; produce the collatz sequence and stop at 1
(defn collatz-stop-at-1 [x]
  (let [cseq (collatz-seq x)]
    (loop [fseq '() cseq cseq]
      (if (= (first cseq) 1)
        (reverse (conj fseq 1))
        (recur (conj fseq (first cseq)) (rest cseq))))))

;; user=> (collatz-stop-at-1 511)
;; (511 1534 767 2302 1151 3454 1727 5182 2591 7774 3887 11662 5831 17494 8747 26242 13121 
;; 39364 19682 9841 29524 14762 7381 22144 11072 5536 2768 1384 692 346 173 520 260 130 65 
;; 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1)