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Sunday, December 12, 2010

Euler problem 14

Easy as long as you remember to use LONG and not INT!

http://projecteuler.net/index.php?section=problems&id=14

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.

________________

static void Main(string[] args)
      {
          long maxl = 0;
          long maxn = 0;
          for (long s = 6; s < 1000000; s++)
          {
             long x = s;
              long l = 1;
              while (x > 1)
              {
                  l++;
                  if (x % 2 == 0)
                  {
                      x = x / 2;
                  }
                  else
                  {
                      x = 3 * x + 1;
                  }

              }
              if (l > maxl)
              {
                  maxn = s; //starting number
                  maxl = l;
              }
          }
      Console.WriteLine(maxl + ","+ maxn);
      Console.ReadLine();

      }

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