A180414 -id:A180414 - cp's OEIS frontend

A048211 Number of distinct resistances that can be produced from a circuit of n equal resistors using only series and parallel combinations.

1, 2, 4, 9, 22, 53, 131, 337, 869, 2213, 5691, 14517, 37017, 93731, 237465, 601093, 1519815, 3842575, 9720769, 24599577, 62283535, 157807915, 400094029, 1014905643, 2576046289, 6541989261, 16621908599, 42251728111, 107445714789, 273335703079

Offset: 1

Tony Bartoletti

Found by exhaustive search. Program produces all values that are combinations of two binary operators a() and b() (here "sum" and "reciprocal sum of reciprocals") over n occurrences of 1. E.g., given 4 occurrences of 1, the code forms all allowable postfix forms, such as 1 1 1 1 a a a and 1 1 b 1 1 a b, etc. Each resulting form is then evaluated according to the definitions for a and b.
Each resistance that can be constructed from n 1-ohm resistors in a circuit can be written as the ratio of two positive integers, neither of which exceeds the (n+1)st Fibonacci number. E.g., for n=4, the 9 resistances that can be constructed can be written as 1/4, 2/5, 3/5, 3/4, 1/1, 4/3, 5/3, 5/2, 4/1 using no numerator or denominator larger than Fib(n+1) = Fib(5) = 5. If a resistance x can be constructed from n 1-ohm resistors, then a resistance 1/x can also be constructed from n 1-ohm resistors. - Jon E. Schoenfield, Aug 06 2006
The fractions in the comment above are a superset of the fractions occurring here, corresponding to the upper bound A176500. - Joerg Arndt, Mar 07 2015
The terms of this sequence consider only series and parallel combinations; A174283 considers bridge combinations as well. - Jon E. Schoenfield, Sep 02 2013

			a(2) = 2 since given two 1-ohm resistors, a series circuit yields 2 ohms, while a parallel circuit yields 1/2 ohms.

Antoni Amengual, The intriguing properties of the equivalent resistances of n equal resistors combined in series and in parallel, American Journal of Physics, 68(2), 175-179 (February 2000). [From _Sameen Ahmed Khan_, Apr 27 2010]
Sameen Ahmed Khan, Mathematica program
Sameen Ahmed Khan, Mathematica notebook for A048211 and A000084
Sameen Ahmed Khan, The bounds of the set of equivalent resistances of n equal resistors combined in series and in parallel, arXiv:1004.3346 [physics.gen-ph], 2010.
Sameen Ahmed Khan, How Many Equivalent Resistances?, RESONANCE, May 2012. - From _N. J. A. Sloane_, Oct 15 2012
Sameen Ahmed Khan, Farey sequences and resistor networks, Proc. Indian Acad. Sci. (Math. Sci.) Vol. 122, No. 2, May 2012, pp. 153-162. - From _N. J. A. Sloane_, Oct 23 2012
Sameen Ahmed Khan, Beginning to Count the Number of Equivalent Resistances, Indian Journal of Science and Technology, Vol. 9, Issue 44, pp. 1-7, 2016.
Marx Stampfli, Bridged graphs, circuits and Fibonacci numbers, Applied Mathematics and Computation, Volume 302, 1 June 2017, Pages 68-79.

Let T(x, n) = 1 if x can be constructed with n 1-ohm resistors in a circuit, 0 otherwise. Then A048211 is t(n) = sum(T(x, n)) for all x (x is necessarily rational). Let H(x, n) = 1 if T(x, n) = 1 and T(x, k) = 0 for all k < n, 0 otherwise. Then A051389 is h(n) = sum(H(x, n)) for all x (x is necessarily rational).
Cf. A153588, A174283, A174284, A174285 and A174286, A176497, A176498, A176499, A176500, A176501, A176502. - Sameen Ahmed Khan, Apr 27 2010
Cf. A180414.

r:= proc(n) option remember; `if`(n=1, {1}, {seq(seq(seq(
      [f+g, 1/(1/f+1/g)][], g in r(n-i)), f in r(i)), i=1..n/2)})
    end:
a:= n-> nops(r(n)):
seq(a(n), n=1..15);  # Alois P. Heinz, Apr 02 2015

r[n_] := r[n] = If[n == 1, {1}, Union @ Flatten @ {Table[ Table[ Table[ {f+g, 1/(1/f+1/g)}, {g, r[n-i]}], {f, r[i]}], {i, 1, n/2}]}]; a[n_] := Length[r[n]]; Table[a[n], {n, 1, 15}] (* Jean-François Alcover, May 28 2015, after Alois P. Heinz *)

\\ not efficient; just to show the method
N=10;
L=vector(N);  L[1]=[1];
{ for (n=2, N,
    my( T = Set( [] ) );
    for (k=1, n\2,
        for (j=1, #L[k],
            my( r1 = L[k][j] );
            for (i=1, #L[n-k],
                my( r2 = L[n-k][i] );
                T = setunion(T,  Set([r1+r2, r1*r2/(r1+r2) ]) );
            );
        );
    );
    T = vecsort(Vec(T), , 8);
    L[n] = T;
); }
for(n=1, N, print1(#L[n], ", ") );
\\ Joerg Arndt, Mar 07 2015

From Bill McEachen, Jun 08 2024: (Start)
(2.414^n)/4 < a(n) < (1-1/n)*(0.318)*(2.618^n) (Khan, n>3).
Conjecture: a(n) ~ K * a(n-1), K approx 2.54. (End)

More terms from John W. Layman, Apr 06 2002
a(16)-a(21) from Jon E. Schoenfield, Aug 06 2006
a(22) from Jon E. Schoenfield, Aug 28 2006
a(23) from Jon E. Schoenfield, Apr 18 2010
Definition edited (to specify that the sequence considers only series and parallel combinations) by Jon E. Schoenfield, Sep 02 2013
a(24)-a(25) from Antoine Mathys, Apr 02 2015
a(26)-a(27) from Johannes P. Reichart, Nov 24 2018
a(28)-a(30) from Antoine Mathys, Dec 08 2024

A337517 a(n) is the number of distinct resistances that can be produced from a circuit with exactly n unit resistors.

Original entry on oeis.org

1, 1, 2, 4, 9, 23, 57, 151, 427, 1263, 3823, 11724, 36048, 110953, 342079, 1064468, 3341067, 10583564, 33727683, 107931482, 346615834

Offset: 0

Rainer Rosenthal and Hugo Pfoertner, Oct 29 2020

One can view a circuit with n unit resistors as a multigraph G with n edges and a pair P of distinguished nodes. Every edge of the graph must be contained in a path connecting the two distinguished nodes.
In case n > 0, a(n) counts all resistances R(G, P), which are rational numbers by Kirchhoff's laws. In case n = 0, the graph G consists of only two pair P nodes, and there is only one resistance: oo = infinity; so a(0) = 1. In the OEIS, there are already sequences that count the possible resistances of circuits of certain types (for the definitions see A337516).
     OEIS  | type |  1  2  3  4   5   6   7    8     9    10    11     12     13
  ---------+------+--------------------------------------------------------------
   A048211 | SP   | [1] 2  4  9  22  53  131  337   869  2213  5691  14517  37017
   A174283 | SPB  |  1  2  4  9  23 [57] 151  415  1157  3191  8687  23199  61677
   A337516 | SPBF |  1  2  4  9  23  57  151 [421] 1202  3397  9498  25970  70005
   A337517 | all  |  1  2  4  9  23  57  151 [427] 1263  3823 11724  36048 110953
The table shows the number of different resistances, which grows with the complexity of the circuits. Values in square brackets mark the beginning of the newly explored range. Values a(n) up to n = 7 are fully classified, and have one of the given types, i.e., they can be computed by the functions Ser(), Par(), Bri(), and Frk() defined in A337516. For a(n), n >= 8, the theory in A180414 has to be applied.
Note: The 'set counted by A180414(n)' is the union of all 'sets counted by A337517(k) for k = 0 .. n'.
Admissible networks (G, P) are those defined in the Karnofsky paper (A180414).

			For a(n) up to n = 7 see the above mentioned sequences.

Wikipedia, Electrical resistance and conductance
Index to sequences related to resistances.

Cf. A048211, A180414, A174283, A337516, A338197.

a(8)-a(14) from Andrew Howroyd, Oct 31 2020
a(15)-a(16) from Hugo Pfoertner, Dec 06 2020
a(17) from Hugo Pfoertner, Dec 09 2020
a(18) from Hugo Pfoertner, Apr 09 2021
a(19) from Zhao Hui Du, May 15 2023
a(20) from Zhao Hui Du, May 23 2023

A174283 Number of distinct resistances that can be produced using n equal resistors in, series, parallel and/or bridge configurations.

Original entry on oeis.org

1, 2, 4, 9, 23, 57, 151, 415, 1157, 3191, 8687, 23199, 61677, 163257, 432541, 1146671, 3039829

Offset: 1

Sameen Ahmed Khan, Mar 15 2010

This sequence is a variation on A048211, which uses only series and parallel combinations. Since a bridge circuit requires minimum of five resistances the first four terms coincide. For the definition of "bridge" see A337516.

			Example 1: Five unit resistors: each arm of the bridge has one unit resistor, leading to an equivalent resistance of 1; so the set is {1} and its order is 1. Thus a(5) = A048211(5) + 1 = 23.
Example 2: Six unit resistors: a bridge with 6 resistors yields A174285(6) = 3 different resistances and the series parallel combinations give A048211(6) = 53 resistances, but resistance 1 is counted twice. The union of the forementioned resistances has cardinality 53+3-1 = 55. There are two more circuits to be considered: the bridge with five unit resistors and the sixth unit resistor either in parallel (value 1/2) or in series (value 2). Both values 1/2 and 2 are not counted by A048211(6) or A174285(6), so the total is 55 + 2 = 57. - _Rainer Rosenthal_, Oct 25 2020

Antoni Amengual, The intriguing properties of the equivalent resistances of n equal resistors combined in series and in parallel, American Journal of Physics, 68(2), 175-179 (February 2000).
Sameen Ahmed Khan, The bounds of the set of equivalent resistances of n equal resistors combined in series and in parallel, arXiv:1004.3346v1 [physics.gen-ph], (20 April 2010).
Sameen Ahmed Khan, Farey sequences and resistor networks, Proc. Indian Acad. Sci. (Math. Sci.) Vol. 122, No. 2, May 2012, pp. 153-162.
Sameen Ahmed Khan, Beginning to Count the Number of Equivalent Resistances, Indian Journal of Science and Technology, Vol. 9, Issue 44, pp. 1-7, 2016.
Hugo Pfoertner, Increase of number of representable resistances by allowing bridges, Plot2 of a(n)/A048211.

Cf. A048211, A153588, A174284, A174285, A174286, A176499, A176500, A176501, A176502, A180414, A337516, A337517.

a(8) corrected and a(9)-a(17) from Rainer Rosenthal, Oct 29 2020

A338197 a(n) is the number of distinct resistances that can be obtained by a network of exactly n equal resistors, but not by any network with fewer than n equal resistors.

Original entry on oeis.org

1, 2, 4, 8, 20, 44, 114, 312, 894, 2639, 8005, 24362, 74918, 231123, 722388, 2276599, 7242497, 23144119, 74203799, 238684352

Offset: 1

Hugo Pfoertner, Nov 03 2020

See A180414 and A337517 for more information and references.

			a(6) = 44 because the resistances 11/13 and 13/11 (in units of resistor value) are representable in addition to the A051389(6)=42 resistances that can be achieved by only serial and parallel configurations with exactly 6 resistors and not by a network with fewer than 6 resistors.

Allan Gottlieb, Oct 3, 2003 addendum (Karnofsky).
Index to sequences related to resistances.

Cf. A051389, A180414, A337517, A338487.

a(n) = A180414(n) - A180414(n-1).

a(n) = A051389(n) for n <= 5, a(n) > A051389(n) otherwise.

a(15) corrected and a(16) added by Hugo Pfoertner, Dec 06 2020
a(17) from Hugo Pfoertner, Dec 09 2020
a(18) from Hugo Pfoertner, Apr 09 2021
a(19) from Zhao Hui Du, May 15 2023
a(20) from Zhao Hui Du, May 23 2023

A174286 Number of distinct resistances that can be produced using at most n equal resistors in series and/or parallel, confined to the five arms (four arms and the diagonal) of a bridge configuration. Since the bridge requires a minimum of five resistors, the first four terms are zero.

Original entry on oeis.org

0, 0, 0, 0, 1, 3, 19, 75, 291, 985, 3011, 8659, 24319, 65899, 176591, 464451, 1211185

Offset: 1

Sameen Ahmed Khan, Mar 15 2010

			Example 1: Five equal unit resistors. Each arm of the bridge has one unit resistor, leading to an equivalent resistance of 1; so the set is {1} and its order is 1. Example 2: Six equal unit resistors. Four arms have one unit resistor each and the fifth arm has two unit resistors. Two resistors in the same arm, when combined in series and parallel result in 2 and 1/2 respectively (corresponding to 2: {1/2, 2} in A048211). The set {1/2, 2}, in the diagonal results in {1}. Set {1/2, 2} in any of the four arms results in {11/13, 13/11}. Consequently, with six equal resistors, we have the set {11/13, 1, 13/11}, whose order is 3. Union of the previous terms is {1} and the union with these three is again {11/13, 1, 13/11}. So the terms for five and six resistors are 1 and 3 respectively.

Antoni Amengual, The intriguing properties of the equivalent resistances of n equal resistors combined in series and in parallel, American Journal of Physics, 68(2), 175-179 (February 2000). Digital Object Identifier (DOI): 10.1119/1.19396.
Sameen Ahmed Khan, The bounds of the set of equivalent resistances of n equal resistors combined in series and in parallel, arXiv:1004.3346v1 [physics.gen-ph], (20 April 2010).
Rainer Rosenthal, Maple programs SetA174285 and SetA174286
Marx Stampfli, Bridged graphs, circuits and Fibonacci numbers, Applied Mathematics and Computation, Volume 302, 1 June 2017, Pages 68-79.
Index to sequences related to resistances.

Cf. A048211, A153588, A174283, A174284, A174285, A180414, A337516, A337517, A338487.

Cf. A176499, A176500, A176501, A176502.

See link section: A174286(n) = nops(SetA174286(n)).

From Stampfli's paper, a(8) corrected and a(9)-a(12) added by Eric M. Schmidt, Sep 09 2017
Name edited by Eric M. Schmidt, Sep 09 2017
a(13)-a(17) added by Rainer Rosenthal, Feb 05 2021

A174284 Number of distinct finite resistances that can be produced using at most n equal resistors (n or fewer resistors) in series, parallel and/or bridge configurations.

Original entry on oeis.org

0, 1, 3, 7, 15, 35, 79, 193, 493, 1299, 3429, 9049, 23699, 62271, 163997, 433433, 1147659, 3040899

Offset: 0

Sameen Ahmed Khan, Mar 15 2010

This sequence is a variation on A153588, which uses only series and parallel combinations. The circuits with exactly n unit resistors are counted by A174283, so this sequence counts the union of the sets, which are counted by A174283(k), k <= n. - Rainer Rosenthal, Oct 27 2020

For n = 0 the resistance is infinite, therefore the number of finite resistances is a(0) = 0. Sequence A180414 counts all resistances (including infinity) and so has A180414(0) = 1 and A180414(n) = a(n) + 1 for all n up to n = 7. For n > 7 the networks get more complex, producing more resistance values, so A180414(n) > a(n) + 1. - Rainer Rosenthal, Feb 13 2021

			Since a bridge circuit requires a minimum of five resistors, the first four terms coincide with A153588. The fifth term also coincides since the set corresponding to five resistors for the bridge, i.e. {1}, is already obtained in the fourth set corresponding to the fourth term in A153588. [Edited by _Rainer Rosenthal_, Oct 27 2020]

Antoni Amengual, The intriguing properties of the equivalent resistances of n equal resistors combined in series and in parallel, American Journal of Physics, 68(2), 175-179 (February 2000).
Sameen Ahmed Khan, The bounds of the set of equivalent resistances of n equal resistors combined in series and in parallel, arXiv:1004.3346v1 [physics.gen-ph], (20 April 2010).
Sameen Ahmed Khan, Farey sequences and resistor networks, Proc. Indian Acad. Sci. (Math. Sci.) Vol. 122, No. 2, May 2012, pp. 153-162.
Sameen Ahmed Khan, Beginning to Count the Number of Equivalent Resistances, Indian Journal of Science and Technology, Vol. 9, Issue 44, pp. 1-7, 2016.
Rainer Rosenthal, Maple program SetA174283 used for A174284
Index to sequences related to resistances.

Cf. A048211, A153588, A174283, A174285, A174286, A176499, A176500, A176501, A176502, A180414.

# SetA174283(n) is the set of resistances counted by A174283(n) (see Maple link).
AccumulatedSetsA174283 := proc(n) option remember;
if n=1 then {1} else `union`(AccumulatedSetsA174283(n-1), SetA174283(n)) fi end:
A174284 := n -> nops(AccumulatedSetsA174283(n)):
seq(A174284(n), n=1..9); # Rainer Rosenthal, Oct 27 2020

a(n) = #(union of all S(k), k <= n), where S(k) is the set which is counted by A174283(k). - Rainer Rosenthal, Oct 27 2020

a(8) corrected, a(9)-a(17) from Rainer Rosenthal, Oct 27 2020

Title changed and a(0) added by Rainer Rosenthal, Feb 13 2021

A338580 Numerators of resistance values that can be obtained from a network of exactly 10 one-ohm resistors, but not from any network with fewer than 10 one-ohm resistors. Denominators are in A338590.

Original entry on oeis.org

1, 2, 3, 3, 4, 5, 5, 4, 5, 6, 7, 6, 5, 7, 8, 7, 7, 8, 7, 11, 9, 10, 11, 10, 13, 9, 11, 10, 11, 13, 12, 9, 11, 13, 13, 11, 9, 12, 13, 11, 14, 10, 11, 15, 9, 14, 16, 17, 7, 8, 19, 11, 12, 13, 14, 15, 18, 19, 16, 15, 14, 13, 12, 21, 9, 8, 15, 20, 19, 17, 11, 19, 14

Offset: 1

Hugo Pfoertner, Nov 06 2020

The A338197(k)/2 initial terms of this sequence are also the numerators of the corresponding sorted lists of resistance values that can be achieved by exactly k resistors for all k < 10.

			See A338590.

Hugo Pfoertner, Table of n, a(n) for n = 1..2639

Cf. A180414, A338197, A338590.

The initial terms of this sequence are also the numerators to be used together with the denominators given in A338595, A338596, A338597, A338598, A338599.

A338600 a(n) is the common denominator of the A338197(n) rational resistance values that can be obtained from a network of exactly n one-ohm resistors, but not by a network of fewer than n one-ohm resistors.

Original entry on oeis.org

1, 2, 6, 60, 840, 360360, 232792560, 5342931457063200, 591133442051411133755680800, 79057815923102180093748328364591874435251553600

Offset: 1

Hugo Pfoertner, Nov 03 2020

nonn

The next terms a(11)=8.87124454467...*10^84 and a(12)=1.80685581583...*10^141 are too big to be included in the data.

			a(4) = 60: The resistance values for which a minimum of 4 resistors is needed are [1/4, 2/5, 3/5, 3/4, 4/3, 5/3, 5/2, 4] with a common denominator of 60.
a(1) = 1: [1],
a(2) = 2: [1/2, 2],
a(3) = 6: [1/3, 2/3, 3/2, 3].

Hugo Pfoertner, Table of n, a(n) for n = 1..15

Cf. A048211, A051389, A180414, A337517, A338197, A338580, A338590, A338595, A338596, A338597, A338598, A338599, A338605, A338606, A338607, A338608, A338609.

A338601 Numerators x of resistance values R=x/y that can be obtained by a network of at most 10 one-ohm resistors such that a network of more than 10 one-ohm resistors is needed to obtain the resistance y/x. Denominators are in A338602.

Original entry on oeis.org

95, 101, 98, 97, 103, 97, 110, 103, 130, 103, 115, 106, 109, 98, 101

Offset: 1

Hugo Pfoertner, Nov 08 2020

The terms are sorted by increasing value of the resistance R(n) = a(n)/A338602(n).
For more information, references, and links, see A180414 and A338573.
Each network for R = p/q is visualized (see link section) as a multigraph with the battery nodes on top and at the bottom, i.e., the battery edge does not have to cross any edges. Any planar network with 10 resistors presented in this way, has a corresponding tiling of a p X q rectangle by 10 squares, and the inverse resistance q/p can be obtained in the same way. According to the definition of a(n) this is not the case here, so there must be crossing edges in every drawing. It should be noticed though, that all the networks (without the battery edge) are planar. - Rainer Rosenthal, Jan 03 2021
Version 2 of the visualization (see link section) shows that all these exceptional networks are extensions of the same network with 8 resistors. It is the graph K_3_3 without the 'battery edge' A-Z and shall be named VG8. This network VG8 has no related squared rectangle, because it has no series-parallel subnets and has resistance 5/4, but there is no such network with resistance 4/5. So, this is the graph, which is mentioned by Karnofsky in his "Addendum": "The smallest non-planar graph has eight resistors.". - Rainer Rosenthal, Feb 13 2021
The reciprocal 101/130 of R(9) = 130/101 needs 12 resistors, while the other 14 reciprocal resistance values can be obtained by networks of 11 resistors. - Rainer Rosenthal, Jan 16 2021

			All fractions for 10 resistors are: 95/106, 101/109, 98/103, 97/98, 103/101, 97/86, 110/91, 103/83, 130/101, 103/80, 115/89, 106/77, 109/77, 98/67, 101/67.
The corresponding networks are shown below, with -(always 1) and +(maximum node number) indicating the nodes where the voltage is applied. Edges marked ==, ||, //, or \\, have 2 resistors in parallel.
.
     95/106        101/109         98/103         97/98         103/101
  -1=======2     -1-------2     -1-------2     -1-------2     -1-------2
   |\     /|      |\     /||     |\     /|      |\     /|      |\     /|
   | \   / |      | \   / ||     | \   / |      | \   / |      | \   / |
   |  \ /  |      |  \ /  ||     |  \ /  |      |  \ /  |      |  \ /  |
   |   4   |      |   4   ||     |   4   |      |   6   4      4   6   |
   |  / \  |      |  / \  ||     |  //\  |      |  / \  |      |  / \  |
   | /  +6 |      | /  +6 ||     | // +6 |      | /  +7 |      | /  +7 |
   |/     \|      |/     \||     |//    \|      |/     \|      |/     \|
   3-------5      3-------5      3-------5      3-------5      3-------5
.
     97/86         110/91         103/83         130/101        103/80
  -1=======2         -1         -1-------2     -1-----2       -1=======2
   |      /|         / \         |      /||     |    /|\       |      /|
   |     / |        /   \        |     4 ||     |   | | |      |     4 |
   |    /  |       2-----3       |    /  ||     |   | | |      |    /| |
   |   6   |      ||\   / \      |   6   ||     |   4-6 |      |   / 6 |
   |  / \  |      || \4/  |      |  / \  ||     |  /  | |      |  /  | |
   | 4  +7 |      ||  \   |      | /  +7 ||     | /  +7 |      | /  +7 |
   |/     \|       \\ +6--5      |/     \||     |/     \|      |/     \|
   3-------5        \\===//      3-------5      3-------5      3-------5
.
    115/89         106/77         109/77          98/67         101/67
     -1          -1-------2     -1-------2     -1-------2     -1-------2
     / \          |      /||     |     //|      |      /|      |      /|
    /   \         |     4 ||     |     4 |      |     6 |      |     6 |
   2-----3        |    /| ||     |    /| |      |    /| |      |    /| |
   |\   / \       |   / 6 ||     |   / 6 |      |   / 7 |      |   / 7 4
   | \6/  |       |  /  | ||     |  /  | |      |  4  | |      |  /  | |
   |  \   |       | /  +7 ||     | /  +7 |      | /  +8 |      | /  +8 |
   |  +7--5       |/     \||     |/     \|      |/     \|      |/     \|
   4------/       3-------5      3-------5      3-------5      3-------5

Allan Gottlieb, Oct 3, 2003 addendum (Karnofsky).
Rainer Rosenthal, Karnofsky's 15 exceptional networks with 10 resistors (Version 2).
Index to sequences related to resistances.

Cf. A180414, A338197, A338573, A338580, A338590, A338602.

Cf. A338581, A338591, A338582, A338592 (similar for n = 11 and n = 12).

A338590 Denominators of resistance values that can be obtained from a network of exactly 10 one-ohm resistors, but not from any network with fewer than 10 one-ohm resistors. Numerators are in A338580.

Original entry on oeis.org

10, 17, 23, 22, 27, 33, 32, 25, 31, 37, 41, 35, 29, 40, 45, 39, 38, 43, 37, 57, 46, 51, 54, 49, 63, 43, 52, 47, 51, 60, 55, 41, 50, 59, 58, 49, 40, 53, 57, 48, 61, 43, 47, 64, 38, 59, 67, 71, 29, 33, 78, 45, 49, 53, 57, 61, 73, 75, 63, 59, 55, 51, 47, 82, 35, 31

Offset: 1

Hugo Pfoertner, Nov 06 2020

			The list of the 2639 = A338197(10) resistance values, sorted by increasing size of R = A338580(n)/a(n), is [1/10, 2/17, 3/23, 3/22, 4/27, 5/33, 5/32, ..., 32/5, 33/5, 27/4, 22/3, 23/3, 17/2, 10]. There are 15 terms for which their reciprocal value is not in the sequence, given in A338601/A338602.

Hugo Pfoertner, Table of n, a(n) for n = 1..2639

Cf. A180414, A338197, A338573, A338580, A338600, A338601, A338602.

Cf. A338595, A338596, A338597, A338599, A338599 (similar for n = 5..10).

Title corrected by Rainer Rosenthal, Feb 14 2021

cp's OEIS Frontend

A048211 Number of distinct resistances that can be produced from a circuit of n equal resistors using only series and parallel combinations.

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A337517 a(n) is the number of distinct resistances that can be produced from a circuit with exactly n unit resistors.

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A174283 Number of distinct resistances that can be produced using n equal resistors in, series, parallel and/or bridge configurations.

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A338197 a(n) is the number of distinct resistances that can be obtained by a network of exactly n equal resistors, but not by any network with fewer than n equal resistors.

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A174286 Number of distinct resistances that can be produced using at most n equal resistors in series and/or parallel, confined to the five arms (four arms and the diagonal) of a bridge configuration. Since the bridge requires a minimum of five resistors, the first four terms are zero.

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A174284 Number of distinct finite resistances that can be produced using at most n equal resistors (n or fewer resistors) in series, parallel and/or bridge configurations.

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A338580 Numerators of resistance values that can be obtained from a network of exactly 10 one-ohm resistors, but not from any network with fewer than 10 one-ohm resistors. Denominators are in A338590.

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A338600 a(n) is the common denominator of the A338197(n) rational resistance values that can be obtained from a network of exactly n one-ohm resistors, but not by a network of fewer than n one-ohm resistors.

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