A338600 -id:A338600 - cp's OEIS frontend

A338607 Resistance values R < 1 ohm, multiplied by a common denominator 232792560 (= A338600(7)), that can be obtained from a network of exactly 7 one-ohm resistors, but not from any network with fewer than 7 one-ohm resistors.

33256080, 42325920, 49884120, 53721360, 62078016, 64664600, 68468400, 71628480, 72747675, 73513440, 81477396, 82162080, 83140200, 85765680, 88682880, 90530440, 95855760, 98017920, 101846745, 106696590, 110270160, 110853600, 121938960, 122522400, 126095970

Offset: 1

Hugo Pfoertner, Nov 05 2020

The list of the A338197(7)/2 = 57 resistance values < 1 ohm is A338587(n)/A338597(n). a(n) = 232792560 * [1/7, 2/11, 3/14, 3/13, 4/15, 5/18, 5/17, ..., 19/21, 11/12, 12/13, 13/14, 14/15, 15/16, 18/19].

Hugo Pfoertner, Table of n, a(n) for n = 1..57

Cf. A180414, A338197, A338587, A338597, A338600, A338605, A338606, A338608, A338609.

A338605 Resistance values R < 1 ohm, multiplied by their common denominator 840 (= A338600(5)), that can be obtained from a network of exactly 5 one-ohm resistors, but not from any network with fewer than 5 one-ohm resistors.

Original entry on oeis.org

168, 240, 315, 360, 480, 525, 600, 672, 700, 720

Offset: 1

Hugo Pfoertner, Nov 03 2020

			The list of resistance values < 1 ohm is A338580(n)/A338595(n). a(n) = 840 * [1/5, 2/7, 3/8, 3/7, 4/7, 5/8, 5/7, 4/5, 5/6, 6/7].

Cf. A051389, A338580, A338595, A338600.

A338608 Resistance values R < 1 ohm, multiplied by a common denominator 5342931457063200 (= A338600(8)), that can be obtained from a network of exactly 8 one-ohm resistors, but not from any network with fewer than 8 one-ohm resistors.

Original entry on oeis.org

667866432132900, 821989454932800, 942870257128800, 1001799648199350, 1124827675171200, 1161506838492000, 1214302603878000, 1257160342838400, 1272126537396000, 1282303549695168, 1385204451831200, 1393808206190400, 1406034593964000, 1438481546132400, 1473912126086400

Offset: 1

Hugo Pfoertner, Nov 06 2020

			The list of the A338197(8)/2 = 156 resistance values < 1 ohm is A338580(n)/A338598(n). a(n) = 5342931457063200 * [1/8, 2/13, 3/17, 3/16, 4/19, 5/23, 5/22, ..., 23/24, 24/25, 25/26, 26/27, 27/28, 30/31, 34/35].

Hugo Pfoertner, Table of n, a(n) for n = 1..156

Cf. A180414, A338197, A338580, A338598, A338600.

Cf. A338605, A338606, A338607, A338609 (similar for n = 5..9).

A338609 Resistance values R < 1 ohm, multiplied by a common denominator 591133442051411133755680800 (= A338600(9)), that can be obtained from a network of exactly 9 one-ohm resistors, but not from any network with fewer than 9 one-ohm resistors.

Original entry on oeis.org

65681493561267903750631200, 78817792273521484500757440, 88670016307711670063352120, 93336859271275442171949600, 102805816008941066740118400, 105559543223466273884943000, 109469155935446506251052000, 112596846105030692143939200, 113679508086809833414554000

Offset: 1

Hugo Pfoertner, Nov 06 2020

			The list of the A338197(9)/2 = 447 resistance values < 1 ohm is A338580(n)/A338599(n). a(n) = 591133442051411133755680800 * [1/9, 2/15, 3/20, 3/19, 4/23, 5/28, ..., 43/44, 45/46, 46/47, 48/49, 50/51, 55/56].

Hugo Pfoertner, Table of n, a(n) for n = 1..447

Cf. A180414, A338197, A338580, A338599, A338600.

Cf. A338605, A338606, A338607, A338608 (similar for n = 5..8).

A338606 Resistance values R < 1 ohm, multiplied by a common denominator 360360 (= A338600(6)), that can be obtained from a network of exactly 6 one-ohm resistors, but not from any network with fewer than 6 one-ohm resistors.

Original entry on oeis.org

60060, 80080, 98280, 108108, 131040, 138600, 150150, 160160, 163800, 166320, 194040, 196560, 200200, 210210, 221760, 229320, 252252, 262080, 280280, 304920, 324324, 327600

Offset: 1

Hugo Pfoertner, Nov 05 2020

			The list of resistance values < 1 ohm is A338580(n)/A338596(n). a(n) = 360360 * [1/6, 2/9, 3/11, 3/10, 4/11, 5/13, 5/12, 4/9, 5/11, 6/13, 7/13, 6/11, 5/9, 7/12, 8/13, 7/11, 7/10, 8/11, 7/9, 11/13, 9/10, 10/11].

Cf. A180414, A338197, A338580, A338596, A338600, A338605, A338607, A338608, A338609.

A180414 Number of different resistances that can be obtained by combining n one-ohm resistors.

Original entry on oeis.org

1, 2, 4, 8, 16, 36, 80, 194, 506, 1400, 4039, 12044, 36406, 111324, 342447, 1064835, 3341434, 10583931, 33728050, 107931849, 346616201

Offset: 0

Vaclav Kotesovec, Sep 02 2010

In "addendum" J. Karnofsky stated the value a(15) = 1064833. In contrast to the terms up to and including a(14), which could all be confirmed, an independent calculation based on a list of 3-connected simple graphs resulted in the corrected value a(15) = 1064835. - Hugo Pfoertner, Dec 06 2020

See A337517 for the number of different resistances that can be obtained by combining /exactly/ n one-ohm resistors. The method used by Andrew Howroyd (see his program in the link section) uses 3-connected graphs with one edge (the 'battery edge') removed. - Rainer Rosenthal, Feb 07 2021

			a(n) counts all resistances that can be obtained with fewer than n resistors as well as with exactly n resistors. Without a resistor the resistance is infinite, i.e., a(0) = 1. One 1-ohm resistor adds resistance 1, so a(1) = 2. Two resistors in parallel give 1/2 ohm, while in series they give 2 ohms. So a(2) is the number of elements in the set {infinity, 1, 1/2, 2}, i.e., a(2) = 4. - _Rainer Rosenthal_, Feb 07 2021

Technology Review's Puzzle Corner, How many different resistances can be obtained by combining 10 one ohm resistors? Oct 3, 2003.

Allan Gottlieb, Oct 3, 2003 addendum (Karnofsky).
Andrew Howroyd, PARI program (includes scripts for other related sequences)
Joel Karnofsky, Solution of problem from Technology Review's Puzzle Corner Oct 3, 2003, Feb 23 2004.
Joel Karnofsky, Mathematica program for resistances, copied from article.
Index to sequences related to resistances.

Cf. A048211, A051389, A174284, A337517, A338197, A338487, A338573, A338580, A338590, A338600.

Cf. A123545, A338511, A338999, A339072.

Mathematica
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(* See link. *)
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a(n) = A174284(n) + 1 for n <= 7, a(n) > A174284(n) + 1 otherwise. - Hugo Pfoertner, Nov 01 2020

a(n) is the number of elements in the union of the sets SetA337517(k), k <= n, counted by A337517. - Rainer Rosenthal, Feb 07 2021

a(15) corrected and a(16) added by Hugo Pfoertner, Dec 06 2020
a(17) from Hugo Pfoertner, Dec 09 2020
a(0) from Rainer Rosenthal, Feb 07 2021
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

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

A338599 Denominators of resistance values < 1 ohm that can be obtained from a network of exactly 9 one-ohm resistors, but not from any network with fewer than 9 one-ohm resistors. Numerators are in A338580.

Original entry on oeis.org

9, 15, 20, 19, 23, 28, 27, 21, 26, 31, 34, 29, 24, 33, 37, 32, 31, 35, 30, 46, 37, 41, 43, 39, 50, 34, 41, 37, 40, 47, 43, 32, 39, 46, 45, 38, 31, 41, 44, 37, 47, 33, 36, 49, 29, 45, 51, 54, 22, 25, 59, 34, 37, 40, 43, 46, 55, 56, 47, 44, 41, 38, 35, 61, 26, 23

Offset: 1

Hugo Pfoertner, Nov 06 2020

			The list of the 894 = A338197(9) resistance values, sorted by increasing size of R = A338580(n)/a(n) = A338609(n)/A338600(9), is the union of [1/9, 2/15, 3/20, ..., 48/49, 50/51, 55/56] and of the corresponding reciprocal resistances > 1 ohm [56/55, 51/50, 49/48, ..., 20/3, 15/2, 9].

Hugo Pfoertner, Table of n, a(n) for n = 1..447

Cf. A338197, A338580, A338600, A338609.

Cf. A338595, A338596, A338597, A338598, A338590 (similar for n = 5..10).

A338595 Denominators of resistance values < 1 ohm that can be obtained from a network of exactly 5 one-ohm resistors, but not from any network with fewer than 5 one-ohm resistors. Numerators are in A338580.

Original entry on oeis.org

5, 7, 8, 7, 7, 8, 7, 5, 6, 7

Offset: 1

Hugo Pfoertner, Nov 03 2020

			The list of the 20 = A051389(5) resistance values, sorted by increasing size of R = A338580(n)/a(n) = A338605(n)/A338600(5) is [1/5, 2/7, 3/8, 3/7, 4/7, 5/8, 5/7, 4/5, 5/6, 6/7] and the reciprocal resistances > 1 ohm [7/6, 6/5, 5/4, 7/5, 8/5, 7/4, 7/3, 8/3, 7/2, 5/1].

Cf. A051389, A338580, A338600, A338605.

Cf. A338596, A338597, A338598, A338599, A338590 (similar for n = 6..10).

A338596 Denominators of resistance values < 1 ohm that can be obtained from a network of exactly 6 one-ohm resistors, but not from any network with fewer than 6 one-ohm resistors. Numerators are in A338580.

Original entry on oeis.org

6, 9, 11, 10, 11, 13, 12, 9, 11, 13, 13, 11, 9, 12, 13, 11, 10, 11, 9, 13, 10, 11

Offset: 1

Hugo Pfoertner, Nov 05 2020

			The list of the 44 = A338197(6) resistance values, sorted by increasing size of R = A338580(n)/a(n) = A338606(n)/A338600(6), is the union of [1/6, 2/9, 3/11, ..., 11/13, 9/10, 10/11] and of the corresponding reciprocal resistances > 1 ohm [11/10, 10/9, 13/11, ..., 11/3, 9/2, 6].

Cf. A338197, A338580, A338600, A338606.

Cf. A338595, A338597, A338598, A338599, A338590 (similar for n = 5..10)

cp's OEIS Frontend

A338607 Resistance values R < 1 ohm, multiplied by a common denominator 232792560 (= A338600(7)), that can be obtained from a network of exactly 7 one-ohm resistors, but not from any network with fewer than 7 one-ohm resistors.

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A338605 Resistance values R < 1 ohm, multiplied by their common denominator 840 (= A338600(5)), that can be obtained from a network of exactly 5 one-ohm resistors, but not from any network with fewer than 5 one-ohm resistors.

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A338608 Resistance values R < 1 ohm, multiplied by a common denominator 5342931457063200 (= A338600(8)), that can be obtained from a network of exactly 8 one-ohm resistors, but not from any network with fewer than 8 one-ohm resistors.

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A338609 Resistance values R < 1 ohm, multiplied by a common denominator 591133442051411133755680800 (= A338600(9)), that can be obtained from a network of exactly 9 one-ohm resistors, but not from any network with fewer than 9 one-ohm resistors.

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A338606 Resistance values R < 1 ohm, multiplied by a common denominator 360360 (= A338600(6)), that can be obtained from a network of exactly 6 one-ohm resistors, but not from any network with fewer than 6 one-ohm resistors.

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A180414 Number of different resistances that can be obtained by combining n one-ohm resistors.

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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.

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A338599 Denominators of resistance values < 1 ohm that can be obtained from a network of exactly 9 one-ohm resistors, but not from any network with fewer than 9 one-ohm resistors. Numerators are in A338580.

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A338595 Denominators of resistance values < 1 ohm that can be obtained from a network of exactly 5 one-ohm resistors, but not from any network with fewer than 5 one-ohm resistors. Numerators are in A338580.

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A338596 Denominators of resistance values < 1 ohm that can be obtained from a network of exactly 6 one-ohm resistors, but not from any network with fewer than 6 one-ohm resistors. Numerators are in A338580.

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