It is straightforward to construct the set of equivalent resistance for circuits constructed from a bunch of four or five equal resistors. But as the bunch size increases it becomes difficult to find the order of the set of equivalent resistances. Even the computer programs runs out of memory. Here we present an analytical result using simple mathematical machinery. The size of the set is shown to be less than 2.618n.
KeywordsResistors series parallel bridge non-planar Fibonacci numbers Haros-Farey sequence integer sequences
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