The formula for the medical ID, but not tested, so post back if any problems, would be
var text Inital = left ([First Name],1);
var text LastThree = left([Last name],3);
var text Med = Right([medical ID]);
$Initial & $LastThree & $Med
Now, you asked if that could be the Record ID. The Te odd Id is a built in automatic field which is a number wheel which sequentially counts up as records are added.
If you want to make a field in that format to actually be the Key field to the table, then typically tha is done by having a field calculated, and then a form rule to copy that to the key field of the table. There is also an advanced technique which can be used in some circumstances to make they key field be a formula field.
Btw, I suggest that the Medical ID field be a text field as opposed to a numeric field as it�s a very large number. I will need to recheck my notes, but I think that the largest number that Quick Base can hold is 14 digits, which is the length of your field in your example. A Text field can be any length.
