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a(n) is the minimum number of unit resistors in a circuit with resistance R = A007305(n)/A007306(n).
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%I #30 Oct 20 2021 20:57:50

%S 1,2,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,5,7,7,

%T 7,7,7,7,7,7,7,7,7,7,7,7,7,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,5,8,8,8,8,

%U 8,8,8,8,8,8,8,8,8,8,8,7,7,8,8,8,8,8,8,8,8,8,8,8

%N a(n) is the minimum number of unit resistors in a circuit with resistance R = A007305(n)/A007306(n).

%C For small values of n, the circuits are planar and correspond to the tiling of rectangles by squares. See A338573 for more information and examples.

%C The earliest nonplanar deviation occurs at a(3173) corresponding to R = 115/204 needing 11 instead of 12 resistors.

%H Hugo Pfoertner, <a href="/A348020/b348020.txt">Table of n, a(n) for n = 1..4096</a>

%Y First 31 terms coincide with A070941.

%Y Cf. A007305, A007306, A113881, A219158, A338573, A347282.

%Y A338579 can be used for a lookup of the position for a given rational R.

%K nonn

%O 1,2

%A _Hugo Pfoertner_, Oct 14 2021