A338608 -id:A338608 - cp's OEIS frontend

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.

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.

A338598 Denominators of resistance values < 1 ohm 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. Numerators are in A338580.

Original entry on oeis.org

8, 13, 17, 16, 19, 23, 22, 17, 21, 25, 27, 23, 19, 26, 29, 25, 24, 27, 23, 35, 28, 31, 32, 29, 37, 25, 30, 27, 29, 34, 31, 23, 28, 33, 32, 27, 22, 29, 31, 26, 33, 23, 25, 34, 20, 31, 35, 37, 15, 17, 40, 23, 25, 27, 29, 31, 37, 37, 31, 29, 27, 25, 23, 40, 17, 15

Offset: 1

Hugo Pfoertner, Nov 06 2020

			The list of the 312 = A338197(8) resistance values, sorted by increasing size of R = A338580(n)/a(n) = A338608(n)/A338600(8), is the union of [1/8, 2/13, 3/17, ..., 27/28, 30/31, 34/35] and of the corresponding reciprocal resistances > 1 ohm [35/34, 31/30, 28/27, ..., 17/3, 13/2, 8].

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

Cf. A338197, A338573, A338580, A338600, A338608.

Cf. A338595, A338596, A338597, A338599, A338590 (similar for n = 5..10).

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.

Original entry on oeis.org

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.

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.

cp's OEIS Frontend

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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A338598 Denominators of resistance values < 1 ohm 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. Numerators are in A338580.

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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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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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