Question 1163501
<pre>

The pattern goes:

Start with 1

Then follow these four rules over and over

Square it. Get 1
Double it. Get 2
Double it. Get 4
Add 1. Get 5

Square it. Get 25
Double it. Get 50
Double it. Get 100
Add 1. Get 101

Square it. Get 10201
Double it. Get 104060401
Double it. Get 208129802
Add 1. Get 208120803

Answer: the next one after 25 was 50.

[This pattern is as good as any.]

Edwin</pre>