Russian variable resistor datasheet

You can use a microcontroller to control a digitally-controlled potentiometer... there are lots to choose from. They vary in their control mechanisms, but there are several available that can be controlled over I2C or SPI.

The MCP4151-103E/P looks to be cheap, through-hole, pretty capable, and is controlled over SPI for instance.

Like gbarry says. The next higher value you find in the Digikey offering is 2 kΩ, so you would need a 6386 Ω resistor in parallel. That is between one end and the wiper, not across the full resistance. 6386 Ω is also an odd value, so you may want to compose that using different standard values as well.

Now the 1523 Ω, how precise does that have to be? You represent it in 4 significant digits, that's 0.1 %. Potmeters are often 20 %, more precise ones can be pretty expensive. So our 2 kΩ can be anywhere between 1600 Ω and 2400 Ω. In the first case your parallel resistor should be 31650 Ω, in the second 4170 Ω. That's a wide range. You could use a 33 kΩ trimming potmeter. Use a multiturn is you want to get the 1523 Ω really precise.

Note that placing another resistor over the potmeter's wiper distorts its linear characteristic.

The greenish curve shows the resistance as a function of the rotation in % for a 2.2 kΩ resistor parallel to a 5 kΩ linear potmeter. The purple curve shows that resistance for the 2 kΩ potmeter plus the 6386 Ω, so that's not so bad after all. The rule for the most linear characteristic is to have the ratio resistor/potmeter as large as possible.