Help!
2003 F-150 5.4L Triton, 7700 w/ 4WD.
Got this code.
Reset.
Have emission test done 1/2 hour after resetting to get new licence sticker.
Clean bill of health, truck ruuns fine, fuel economy fine, no change.

is there a problem?
Okay to continue driving with dashboard light on?

 

It is an O2 sensor going out. The front one on the passenger side. As far as I know, it won't damage to keep driving it for a bit.

 

Driving it will not hurt the truck. Bear in mind that any new codes will not get your attention as you are ignoring the light because of this. All the heater does is quickly heat up the sensor so the PCM can use it sooner. Start up emissions are effected because it takes longer to heat up using only the exhaust gases. Check the connector pins for corrosion. Was any transmission work done to the vehicle. A wire to the heater may have been pinched and it is cut or shorted out.

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P0135 Heated O2 Sensor Heater Circuit Malfunction (Bank 1, Sensor 1)
P0135 Upstream Heated Oxygen Sensor Heater circuit fault - Bank No. 1

Yea, that's usually the wire, like JMC posted. The White's are the heaters, heats to 800c/1100f/ Grey is ground (PCM ground , directly) / Black is signal not ground.