A347282 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..8.

Hugo Pfoertner, Examples of networks corresponding to a(1)-a(8), October 2021.

Index to sequences related to resistances.

EXAMPLE

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

CROSSREFS

Cf. A007305, A007306, A342558, A348020.

Sequence in context: A355045 A357800 A004459 * A004507 A296760 A297290

Adjacent sequences: A347279 A347280 A347281 * A347283 A347284 A347285

KEYWORD

nonn,hard,more

AUTHOR

Hugo Pfoertner, Oct 12 2021

STATUS

approved