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
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].
Cf.
A048211,
A051389,
A180414,
A337517,
A338197,
A338580,
A338590,
A338595,
A338596,
A338597,
A338598,
A338599,
A338605,
A338606,
A338607,
A338608,
A338609.
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
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].
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
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
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].
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
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].
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
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].
Showing 1-6 of 6 results.
Comments