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  • Euler 14.

    From B. Pym@21:1/5 to All on Tue May 28 11:33:16 2024
    The following iterative sequence is defined for the set of positive
    integers:

    n -> n/2 (n is even)
    n -> 3n + 1 (n is odd)

    Using the rule above and starting with 13, we generate the following
    sequence:

    13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1

    It can be seen that this sequence (starting at 13 and
    finishing at 1) contains 10 terms. Although it has not been
    proved yet (Collatz Problem), it is thought that all starting
    numbers finish at 1.

    Which starting number, under one million, produces the longest chain?

    NOTE: Once the chain starts the terms are allowed to go above one
    million.


    Gauche Scheme

    (use gauche.collection) ;; find-max


    (define (cltz n) (if (odd? n) (+ 1 (* n 3)) (/ n 2)))

    (define (d c n)
    (if (= n 1) c (d (+ 1 c) (cltz n))))

    (find-max (lrange 1 1000000) :key (pa$ d 1))

    ===>
    837799

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