https://www.youtube.com/watch?v=VKcLUqv4ReI

n-and-n-cubed.janet

(defn num-digits
  [x]
  (if (= x 0)
    1
    (math/floor (inc (math/log10 x)))))

(comment

  (num-digits 0)
  # =>
  1

  (num-digits 1)
  # =>
  1

  (num-digits 2)
  # =>
  1

  (num-digits 9)
  # =>
  1

  (num-digits 10)
  # =>
  2

  (num-digits 11)
  # =>
  2

  (num-digits 19)
  # =>
  2

  (num-digits 20)
  # =>
  2

  (num-digits 99)
  # =>
  2

  (num-digits 100)
  # =>
  3

  (num-digits 101)
  # =>
  3

  )

#
(defn digits
  [x]
  (def n-dig (num-digits x))
  (var remaining x)
  (def results @[])
  (loop [i :down-to [(dec n-dig) 0]]
    (def pow-ten (math/pow 10 i))
    (def digit (div remaining pow-ten))
    (array/push results digit)
    (-= remaining (* digit pow-ten)))
  results)

(comment

  (digits 123)
  # =>
  @[1 2 3]

  (digits 0)
  # =>
  @[0]

  (digits 100)
  # =>
  @[1 0 0]

  (digits 300)
  # =>
  @[3 0 0]

  (digits (* 300 300 300))
  # =>
  @[2 7 0 0 0 0 0 0]

  )

(defn digits-to-num
  [digs]
  (var total 0)
  (def num-digs (length digs))
  (loop [i :range [0 num-digs]
         :let [exponent (- (dec num-digs) i)
               pow-ten (math/pow 10 exponent)
               digit (get digs i)
               value (* pow-ten digit)]]
    (+= total value))
  total)

(comment
  
  (digits-to-num @[1 2 3])
  # =>
  123

  (digits-to-num @[0])
  # =>
  0

  )

(defn do-problem
  [start end]
  (seq [i :range-to [start end]
        :let [cubed (* i i i)
              digs (digits cubed)
              last-three (array/slice digs -4 -1)
              added (digits-to-num last-three)]
        :when (= added i)]
    [i cubed]))

(comment

  (do-problem 100 300)
  # =>
  @[[125 1953125]
    [249 15438249]
    [251 15813251]]

  (do-problem 100 1000)
  # =>
  @[[125 1953125]
    [249 15438249]
    [251 15813251]
    [375 52734375]
    [376 53157376]
    [499 124251499]
    [501 125751501]
    [624 242970624]
    [625 244140625]
    [749 420189749]
    [751 423564751]
    [875 669921875]
    [999 997002999]]

  )

(defn do-n-problem
  [start end n]
  (seq [i :range-to [start end]
        :let [cubed (* i i i)
              digs (digits cubed)
              last-n (array/slice digs (- (inc n)) -1)
              added (digits-to-num last-n)]
        :when (= added i)]
    [i cubed]))

(comment

  (do-n-problem 100 300 3)
  # =>
  @[[125 1953125] 
    [249 15438249] 
    [251 15813251]]

  (do-n-problem 100 1000 3)
  # =>
  @[[125 1953125]
    [249 15438249]
    [251 15813251]
    [375 52734375]
    [376 53157376]
    [499 124251499]
    [501 125751501]
    [624 242970624]
    [625 244140625]
    [749 420189749]
    [751 423564751]
    [875 669921875]
    [999 997002999]]

  (do-n-problem 100 10000 4)
  # =>
  @[[624 242970624] 
    [625 244140625] 
    [1249 1948441249] 
    [3751 52776573751] 
    [4375 83740234375] 
    [4999 124925014999] 
    [5001 125075015001] 
    [5625 177978515625] 
    [6249 244023456249] 
    [8751 670151588751] 
    [9375 823974609375] 
    [9376 824238309376] 
    [9999 999700029999]]

  )