20,6,4,3,2,2,2 etc.
10,4,3,2,2,2etc.
16,5,2,2,2 etc.
60,12,6,4,3,2,2etc.

Each sequence follows the exact same rule and when it says 'etc.' the last digit is repeated an infinite number of times. (The first number in each sequence is random and does not follow the rule).

What is the rule for these sequences?

Each successive number is the number of factors in the preceding number:

60 has 12: 1,2,3,4,5,10,12,15,20,30,60
20 has 6: 1,2,4,5,10,20
16 has 5: 1,2,4,8,16
12 has 6: 1,2,3,4,6,12
10 has 4: 1,2,5,10
6 has 4: 1,2,3,6
5 has 2: 1,5
4 has 3: 1,2,4
3 has 2: 1,3
2 has 2: 1,2

I imagine that unless the randomly chosen first number is 1, the sequence will always collapse into an infinite sequence of 2's, starting right after the first prime number is reached.

Posted by Trevor Leitch on 2003-10-26 14:58:47