Timer for turning LED's on for 4 seconds and then off for about 200 seconds
If you don't want to use a tiny microcontroller (PIC10F family is good), you can do what you want by cascading two timers.

Have a look at the datasheet for a CD4060.  This is a CMOS multi-stage binary divider chip with built-in oscillator.  You can configure that chip to have a total period of 200 seconds.

The output of that chip feeds the trigger input of a TLC555 CMOS 555 timer chip via a coupling capacitor.  You can set the ON-time of the 555 to 4 seconds.

But using a PIC10F chip is much, much smaller and would consume less current.  I really like the PIC10F322 - very, very nice chip in a SOT23-6 package.