A347282 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.

18, 19, 20, 18, 26, 19, 17, 19

Offset: 1

Author

Hugo Pfoertner, Oct 12 2021

Keywords

• nonn
• hard
• more

Comments

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

Examples

			  n  A007305(n)/ a(n)   Edge list of network graph (example)
     A007306(n)
  1     1/1       18    [[1, 5], [1, 6], [1, 7], [2, 5], [2, 7], [2, 8],
                         [3, 6], [3, 7], [3, 8], [3, 9], [10, 6], [4, 8],
                         [4, 9], [5, 8], [5, 9], [6, 9], [7, 9], [10, 4]]
                        Poles: [5, 10]
  2     1/2       19    see linked file for description of solutions
  3     1/3       20
  4     2/3       18
  5     1/4       26
  6     2/5       19
  7     3/5       17
  8     3/4       19
  9     1/5    unknown
		

Links

• Hugo Pfoertner, Examples of networks corresponding to a(1)-a(8), October 2021.
• Index to sequences related to resistances.

Crossrefs

Cf. A007305, A007306, A342558, A348020.