%I #15 Jun 06 2024 06:12:24

%S 18,19,20,18,26,19,17,19

%N a(n) is the least number of unit resistors in an electrical network with total resistance A007305(n)/A007306(n) such that all currents through the resistors are distinct and > 0.

%C The trivial case of a single resistor is excluded, thus making a(1) = A342558(18) = 18.

%H Hugo Pfoertner, <a href="/A347282/a347282.txt">Examples of networks corresponding to a(1)-a(8)</a>, October 2021.

%H <a href="/index/Res#resistances">Index to sequences related to resistances</a>.

%e n A007305(n)/ a(n) Edge list of network graph (example)

%e A007306(n)

%e 1 1/1 18 [[1, 5], [1, 6], [1, 7], [2, 5], [2, 7], [2, 8],

%e [3, 6], [3, 7], [3, 8], [3, 9], [10, 6], [4, 8],

%e [4, 9], [5, 8], [5, 9], [6, 9], [7, 9], [10, 4]]

%e Poles: [5, 10]

%e 2 1/2 19 see linked file for description of solutions

%e 3 1/3 20

%e 4 2/3 18

%e 5 1/4 26

%e 6 2/5 19

%e 7 3/5 17

%e 8 3/4 19

%e 9 1/5 unknown

%Y Cf. A007305, A007306, A342558, A348020.

%K nonn,hard,more

%O 1,1

%A _Hugo Pfoertner_, Oct 12 2021