A339548 1 - 1/a(n) is the largest resistance value of this form that can be obtained from a resistor network of not more than n one-ohm resistors.
2, 3, 4, 7, 11, 19, 35, 56, 105, 177, 321, 610, 1001, 1893, 3186, 5714, 10073, 18506
Offset: 2
Examples
The resistor networks from which the target resistance R = 1 - 1/a(n) can be obtained correspond to simple or multigraphs whose edges are one-ohm resistors. Parallel resistors on one edge are indicated by an exponent > 1 after the affected vertex pair. The resistance R occurs between vertex number 1 and the vertex with maximum number in the graph. In some cases there are other possible representations in addition to the representation given.
.
resistors vertices
| R | edges
2 1/2 2 [1,2]^2
3 2/3 3 [1,2],[1,3],[2,3]
4 3/4 4 [1,2],[1,4],[2,3],[3,4]
5 6/7 4 [1,2]^2,[1,3],[2,4],[3,4]
6 10/11 5 [1,2],[1,3],[1,4],[2,3],[3,5],[4,5]
7 18/19 5 [1,2],[1,3]^2,[2,4],[3,4],[3,5],[4,5]
8 34/35 6 [1,2],[1,3],[1,4],[2,5],[3,4],[3,5],[4,6],[5,6]
9 55/56 6 [1,2]^2,[1,3],[2,4],[3,5],[3,6],[4,5],[4,6],[5,6]
10 104/105 7 [1,4],[1,5],[2,4],[2,6],[2,7],[3,5],[3,6],[3,7],[4,6],[5,7]
11 176/177 7 [1,4],[1,6],[2,4],[2,5],[2,7],[3,5],[3,6],[3,7],[4,6],[4,7],
[5,7]
12 320/321 7 [1,4],[1,6],[2,4],[2,5],[2,6],[2,7],[3,4],[3,5],[3,6],[4,6],
[4,7],[5,7]
13 609/610 8 [1,4],[1,5],[1,7],[2,5],[2,6],[2,7],[3,4],[3,6],[3,7],[4,5],
[4,6],[6,8],[7,8]
14 1000/1001 8 [1,4],[1,5],[1,7],[2,4],[2,5],[2,6],[2,7],[3,5],[3,6],[3,7],
[4,5],[4,6],[4,8],[6,8]
15 1892/1893 9 [1,4],[1,5],[2,5],[2,6],[2,7],[2,9],[3,6],[3,7],[3,8],[3,9],
[4,7],[4,8],[4,9],[5,8],[6,8]
16 3185/3186 9 [1,2],[1,3],[2,6],[2,7],[2,9],[3,6],[3,7],[3,8],[4,5],[4,7],
[4,8],[5,6],[5,8],[5,9],[6,7],[8,9]
17 5713/5714 10 [1,2],[1,3],[2,4],[2,5],[2,7],[3,4],[3,6],[3,10],[4,8],[5,6],
[5,7],[5,9],[6,8],[7,8],[7,9],[8,10],[9,10]
18 10072/10073 10 [1,2],[1,3],[2,4],[2,5],[2,6],[3,4],[3,5],[3,10],[4,8],[5,7],
[5,9],[6,7],[6,8],[6,9],[7,8],[7,9],[8,10],[9,10]
19 18505/18506 11 [1,2],[1,3],[2,5],[2,6],[2,7],[3,4],[3,5],[3,11],[4,6],[4,7],
[5,8],[5,10],[6,8],[6,9],[7,9],[7,10],[8,9],[9,11],[10,11]
Links
- Fedor Karpelevitch, Program output: lower.txt
- Fedor Karpelevitch, Program, run with `./gradlew cir2 --args=best`
Crossrefs
Extensions
a(18) from Hugo Pfoertner, Apr 09 2021
a(19) from Fedor Karpelevitch, Aug 17 2025
Comments