Answer to the Problem of the Week

for the week of April 10, 2000

The Number Sequence Problem
What is the next number in this sequence?
4, 16, 37, 58, 89, 145, 42, 20, ...


Solution:

The next number would be 4, and the sequence would repeat.

Each number represents the sum of the squares of the individual digits that compose the preceding digits.

4^2 = 16
1^2 + 6^2 = 37
3^2 + 7^2 = 58
5^2 + 8^2 = 89 etc.


Correctly solved by:

1. Tom Marino Winchester, VA
2. Richard Mocarski Winchester, VA
3. Josh Grewal Winchester, VA