What are good algorithms for detecting abnormality?

Background

Here is the problem:

1. A black box outputs a new number each day.
2. Those numbers have been recorded for a period of time.
3. Detect when a new number from the black box falls outside the pattern of numbers established over the time period.

The numbers are integers, and the time period is a year.

Question

What algorithm will identify a pattern in the numbers?

The pattern might be simple, like always ascending or always descending, or the numbers might fall within a narrow range, and so forth.

Ideas

I have some ideas, but am uncertain as to the best approach, or what solutions already exist:

• Machine learning algorithms?
• Neural network?
• Classify normal and abnormal numbers?
• Statistical analysis?