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The resistor networks considered here correspond to multigraphs in which each edge is replaced by one or more one-ohm resistors, and in which there are two distinguished nodes, called poles, between which there is a total resistance of 1 ohm.

It was known that the smallest resistor network with all currents being distinct consists of 21 resistors, found by Duijvestin in 1978. This assumes that the network is planar and thus the analogy to the perfectly tiled squares exists, see A014530. For history and references see link to Stuart Anderson's website "SPSS, Order 21".

In 1983, A. Augusteijn and A. J. W. Duijvestijn described networks in which the number of resistors in a network with distinct resistances was reduced to 20 by allowing the tiled square to be wrapped onto a cylinder. (see links to their publication and to Stuart Anderson's website "Simple Perfect Square-Cylinders")

For values of n greater than 21 increasingly numerous square divisions with a(n) = n exist so that a(n) = n holds for all n > 21 (see A006983).

In the present sequence, networks based on non-planar graphs are allowed, which makes it possible to find networks with a(n) = n also for n = 18 and n = 19.

In the range from n = 13 to n = 17, larger numbers of distinct currents are found than are possible with the methods for generating Mrs. Perkins's quilts, which naturally correspond to planar graphs.