Minimum number of numbers to express every integer below N as a sum

[CricK0es]

Homework Statement

I am actually trying to create a load bank that has a range from 0 ohms (no resistors with negligible losses in wires) up to a specified value, N, that increases in value by 1 ohm at each setting to cover all the integers in the range . I want to minimise the number of resistors required for said bank without repetition. I would use python to simulate resistors being switched off and on the path of the current.

Is there some mathematical algorithmn or suggested reading that would help me determine this?

Relevant Equations

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I have found code to find simply the minimum numbers needed, but I need to do it without repetition given the nature of an electric circuit. I hope that is a sufficient enough explanation of the problem. Despite being an engineering project this aspect is more mathematical.

 

[phinds]

just use binary values

 

[phyzguy]

I had the same thought as @phinds . So you need 1 Ohm, 2 Ohms, 4 Ohms, 8 Ohms, ... I don't think you can reduce the number of resistors to less than this.

 

[haruspex]

Binary is certainly right if they can only be arranged in series, but is that the case here?

 

[CricK0es]

Yes they are assumed to only be in series with relays that will ON/OFF as the test cycle is performed. Thank you all!