In the following sequence, consisting of positive integers, the first term is a one digit number.

?, ? , 65, 61, 37, 58, 89, 145, ...

A) What is the first term?

B) What is the next term that is a one digit number?

Regardless of what number you start with, using the procedure from the solution, you will eventually get into either a continuous repetition of 1, or a cycle consisting of the numbers 4 16 37 58 89 145 42 20, beginning at some number within this cycle.

Starting with one of: 1, 7, 10, 13, 19, 23, 28, 31, 32 ... eventually (quickly actually) leads to the repetition of 1's. Other numbers smaller than 31 lead to the cycle that includes 4. I don't see a particular pattern of what leads to the 1's and what leads to the 4-etc.-cycle.

Posted by Charlie on 2003-07-15 09:35:21