I can say I have never seen a 13 1/2 watt Fluorescent bulb before.
But I have now.

I wonder what advantage a 13 and 1/2 watt was.
Is this a little shorter than a 14 watt bulb?
Is this the T8 replacement for the 14 T12?

http://www.ebay.com/itm/GE-F13-5T5-CW-FLUORESCENT-TUBE-COOL-WHITE-1-TUBE-ONLY-/121291850069?
pt=US_Light_Bulbs&hash=item1c3d8ec155



15 watt
http://www.ebay.com/itm/1-Sylvania-Fluorescent-Tube-F15T12-WWX-18-NOS-/111259518900?pt=US_Light_Bulbs&hash=item19e79587b4

The seller can't seem to be able to decide who made the lamp

Or whether it's a T8 or T5. 

A few members here have F13.5T8 lamps. Weird lamp, as it's the same length as an F13T8, and only half a watt more. Not sure what the point of such a lamp would've been. There's also an F10T8, which is also the same size of an F13T8!

Or whether it's a T8 or T5.  

A few members here have F13.5T8 lamps. Weird lamp, as it's the same length as an F13T8, and only half a watt more. Not sure what the point of such a lamp would've been. There's also an F10T8, which is also the same size of an F13T8!

Wow, may be there was some confusion in the engineering department.
I would guess that they rounded up or down the numbers in the past lamps as I don't see how they could come out exact on wattage.
A half a watt seems to be a little over engineering.

May be they could not decide if it used 13 watts or 14 watts, so they struck a compromise and called it 13 1/2 watts.
 

I have six under cabinet lights that use F13T5s.  They run on 14, 15, 20 watt "choke" ballasts.  I have a couple F13.5T5 tubes too and cant tell a lick of difference in them and the 13 watt.