A338597 -id:A338597 - cp's OEIS frontend

A338587 Numerators of resistance values < 1 ohm 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. Denominators are in A338597.

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

Offset: 1

Hugo Pfoertner, Nov 05 2020

			The list of the 114 = A338197(7) resistance values, sorted by increasing size of R = a(n)/A338597(n) = A338607(n)/A338600(7), is the union of [1/7, 2/11, 3/14, ..., 14/15, 15/16, 18/19] and of the corresponding reciprocal resistances > 1 ohm [19/18, 16/15, 15/14, ..., 14/3, 11/2, 7].

Cf. A338197, A338597, A338607.

Cf. A338595, A338596, A338598, A338599, A338590 (similar for n = 5..10).

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.

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)

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.

cp's OEIS Frontend

A338587 Numerators of resistance values < 1 ohm 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. Denominators are in A338597.

Views

Author

Keywords

Examples

Crossrefs

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.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

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.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

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.

Views

Author

Keywords

Examples

Links

Crossrefs

Extensions

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.

Views

Author

Keywords

Examples

Links

Crossrefs

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.

Views

Author

Keywords

Examples

Crossrefs

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.

Views

Author

Keywords

Examples

Crossrefs

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.

Views

Author

Keywords

Examples

Links

Crossrefs

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.

Views

Author

Keywords

Comments

Links

Crossrefs