I think this may be a typical problem with converting to a Noma programmable thermostat.
I currently have a Sears model , 4 wire and a black wire (jumper?) going from RC to 4. There is also a disabled black wire coming from the wall but not connected to anything.
Do I eliminate the black jumper wire and take the black wire from the wall and connect this to the RH?

Are these programmable thermostats worth all the confusion of setting up and programming?

Thanks for any help.

I sometimes wonder that myself. You only need to go through the connection and set up once. 4? Typical of Sears not to use others conventions.

Usually there is a 24 volt AC transformer in the furnace with the secondary winding connected to a red wire running to the thermostat and a blue wire, common, to the gas valve, A/C relay, and fan relay. From the thermostat there will be white wire to the gas valve, yellow to the A/C, and green to the fan. The thermostat is wired to switch the power from the red to the white, yellow, and green as needed with the blue completing the circuit. Most thermostats and furnaces have the contacts labeled R, B or C, W, Y, and G for the corresponding wire colors. Many have RH and RC to allow separate transformers for heating and cooling. With just one red wire, jumper them. It may be wired to have the A/C control wires return to the furnace and its controls and then a second wire goes to the A/C unit. Internal wiring may replace the green wire if the thermostat does not give you the option of fan only or continuous fan. Digital or programmable thermostats may need the blue wire connected to them.

So if you have both RH and RC, the red wire needs to be connected to both. If the Noma has a common, the disabled black wire can be used to connect it to the common terminal of the transformer.

'4' is probably same as RH. You can try using the jumper to connect Rc and Rh to see if it work.