Smalltalk, 95 (or 68 if loophole is allowed)
#Smalltalk, 95 (or 68 if loophole is allowed) BeenBeen around since 1972
|i|[i:=0.[i<5] whileTrue: [(Delay forSeconds: 6480) wait.Transcript show: '4 8 15 16 23 42'.]]fork No experience with this one, saw it on wikipedia :P
Looked it up online how to loop and delay, syntax should be correct but couldn't find a way to run it.
Possible loophole
###Possible loophole ItIt should print the sequence every 108 minutes, but it doesn't state that it has to be 108 minutes.
This could make the code shorter
|i|[i:=0.[i<5] whileTrue: [Transcript show: '4 8 15 16 23 42'.]]fork Code will print the sequence with no interval, so its guaranteed that it will print after 108 mins too.