perplexus.info :: Numbers : Some definite results

Some definite results (Posted on 2015-09-17)

Find the possible outcomes of the following algorithm:

1.Take a random positive integer, divisible by three.
2.Consider its base 10 digits.
3.Take the sum of their cubes.
4.Go back to step 2.

Rem: You may limit your research for n<1000.

See The Solution Submitted by Ady TZIDON

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re: non-analytic solution

| Comment 4 of 5 |

(In reply to non-analytic solution by Paul)

I also do not know much about Ruby, but my Basic solution finds that at most 13 iterations are required to reach 153. Perhaps what you found is that 14 iterations are required to get two successive numbers that are equal; that is, to get the second 153.

DefDbl A-Z

Dim crlf$

Private Sub Form_Load()

Form1.Visible = True

Text1.Text = ""

crlf = Chr$(13) + Chr$(10)

For n = 3 To 10000 Step 3

DoEvents

' Text1.Text = Text1.Text & n & " "

n1 = n

For iter = 1 To 15

ns$ = LTrim(Str(n1))

n1 = 0

For i = 1 To Len(ns)

v = Val(Mid(ns, i, 1))

n1 = n1 + v * v * v

' Text1.Text = Text1.Text & Str(n1)

If n1 = 153 Then Exit For

DoEvents

Next iter

If iter > 12 Then Text1.Text = Text1.Text & n & Str(n1) & Str(iter) & crlf

' Text1.Text = Text1.Text & crlf & crlf

Text1.Text = Text1.Text & crlf & n & " done"

End Sub

Column 1 of the following list shows the starting numbers that require 13 iterations. The other columns merely verify that 153 has been reached and that 13 is the number of iterations. Any number of iterations greater than 12 are reported and only 13's show up.

177 153 13

717 153 13

771 153 13

1077 153 13

1707 153 13

1770 153 13

4467 153 13

4476 153 13

4647 153 13

4674 153 13

4677 153 13

4746 153 13

4764 153 13

4767 153 13

4776 153 13

4779 153 13

4797 153 13

4977 153 13

6447 153 13

6474 153 13

6477 153 13

6744 153 13

6747 153 13

6774 153 13

7017 153 13

7071 153 13

7107 153 13

7170 153 13

7446 153 13

7464 153 13

7467 153 13

7476 153 13

7479 153 13

7497 153 13

7644 153 13

7647 153 13

7674 153 13

7701 153 13

7710 153 13

7746 153 13

7749 153 13

7764 153 13

7794 153 13

7947 153 13

7974 153 13

9477 153 13

9747 153 13

9774 153 13

Posted by Charlie on 2015-09-18 08:27:49

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