cp's OEIS Frontend

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.

%I A339548 #32 Aug 20 2025 14:23:55
%S A339548 2,3,4,7,11,19,35,56,105,177,321,610,1001,1893,3186,5714,10073,18506
%N 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.
%H A339548 Fedor Karpelevitch, <a href="https://github.com/fedork/saigon_kt/blob/main/lower.txt">Program output: lower.txt</a>
%H A339548 Fedor Karpelevitch, <a href="https://github.com/fedork/saigon_kt/blob/main/src/main/kotlin/Main7.kt">Program</a>, run with `./gradlew cir2 --args=best`
%e A339548 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.
%e A339548 .
%e A339548 resistors      vertices
%e A339548    |     R        |  edges
%e A339548    2     1/2      2 [1,2]^2
%e A339548    3     2/3      3 [1,2],[1,3],[2,3]
%e A339548    4     3/4      4 [1,2],[1,4],[2,3],[3,4]
%e A339548    5     6/7      4 [1,2]^2,[1,3],[2,4],[3,4]
%e A339548    6    10/11     5 [1,2],[1,3],[1,4],[2,3],[3,5],[4,5]
%e A339548    7    18/19     5 [1,2],[1,3]^2,[2,4],[3,4],[3,5],[4,5]
%e A339548    8    34/35     6 [1,2],[1,3],[1,4],[2,5],[3,4],[3,5],[4,6],[5,6]
%e A339548    9    55/56     6 [1,2]^2,[1,3],[2,4],[3,5],[3,6],[4,5],[4,6],[5,6]
%e A339548   10   104/105    7 [1,4],[1,5],[2,4],[2,6],[2,7],[3,5],[3,6],[3,7],[4,6],[5,7]
%e A339548   11   176/177    7 [1,4],[1,6],[2,4],[2,5],[2,7],[3,5],[3,6],[3,7],[4,6],[4,7],
%e A339548                     [5,7]
%e A339548   12   320/321    7 [1,4],[1,6],[2,4],[2,5],[2,6],[2,7],[3,4],[3,5],[3,6],[4,6],
%e A339548                     [4,7],[5,7]
%e A339548   13   609/610    8 [1,4],[1,5],[1,7],[2,5],[2,6],[2,7],[3,4],[3,6],[3,7],[4,5],
%e A339548                     [4,6],[6,8],[7,8]
%e A339548   14  1000/1001   8 [1,4],[1,5],[1,7],[2,4],[2,5],[2,6],[2,7],[3,5],[3,6],[3,7],
%e A339548                     [4,5],[4,6],[4,8],[6,8]
%e A339548   15  1892/1893   9 [1,4],[1,5],[2,5],[2,6],[2,7],[2,9],[3,6],[3,7],[3,8],[3,9],
%e A339548                     [4,7],[4,8],[4,9],[5,8],[6,8]
%e A339548   16  3185/3186   9 [1,2],[1,3],[2,6],[2,7],[2,9],[3,6],[3,7],[3,8],[4,5],[4,7],
%e A339548                     [4,8],[5,6],[5,8],[5,9],[6,7],[8,9]
%e A339548   17  5713/5714  10 [1,2],[1,3],[2,4],[2,5],[2,7],[3,4],[3,6],[3,10],[4,8],[5,6],
%e A339548                     [5,7],[5,9],[6,8],[7,8],[7,9],[8,10],[9,10]
%e A339548   18 10072/10073 10 [1,2],[1,3],[2,4],[2,5],[2,6],[3,4],[3,5],[3,10],[4,8],[5,7],
%e A339548                     [5,9],[6,7],[6,8],[6,9],[7,8],[7,9],[8,10],[9,10]
%e A339548   19 18505/18506 11 [1,2],[1,3],[2,5],[2,6],[2,7],[3,4],[3,5],[3,11],[4,6],[4,7],
%e A339548                     [5,8],[5,10],[6,8],[6,9],[7,9],[7,10],[8,9],[9,11],[10,11]
%Y A339548 Cf. A180414, A337517, A339808.
%Y A339548 Cf. A279317, showing that maximum solutions using the square packing analogy can only be obtained for n <= 11 resistors.
%K A339548 nonn,hard,more
%O A339548 2,1
%A A339548 _Hugo Pfoertner_, Dec 12 2020
%E A339548 a(18) from _Hugo Pfoertner_, Apr 09 2021
%E A339548 a(19) from _Fedor Karpelevitch_, Aug 17 2025