An URL very similar to the now defunct "JreCurrentVersion2.txt":
http://javadl-esd-secure.oracle.com/update/baseline.version
The contents of the link look like this:
1.8.0_111
1.7.0_121
1.6.0_131
1.5.0_99
1.4.2_43
You can easily parse the contents to find the latest JRE versions.