A340708 - OEIS

%I #30 Apr 19 2021 10:30:22

%S 1,2,3,5,8,13,24,40,69,130,231,408,689,1272,2153,3960,6993,12560

%N Maximum denominator of resistances obtained by an electrical network with n unit resistors.

%C a(n) is taken from the set of resistance values counted by A337517(n). These sets can be computed by the PARI program of Andrew Howroyd in A180414.

%C Also the maximum numerator of these electrical networks for small n.

%C Maximum numerator and maximum denominator coincide for planar networks: for every resistance R in a planar network with n resistors there is always another planar network with n resistors and resistance 1/R. For nonplanar networks this is not necessarily so, as can be seen in A338573.

%C The asymmetry is illustrated by the example a(15) = 2153.

%C The author conjectures that this asymmetry will increase with n, and eventually the maxima will differ.

%C Conjecture: a(19) = 22233, a(20) = 39918. It would be very desirable to know at which value of n > 18 the maximum values of numerators and denominators differ for the first time. - _Hugo Pfoertner_, Apr 19 2021

%H <a href="/index/Res#resistances">Index to sequences related to resistances</a>.

%e Denominators for numerator a(15) = 2153 in electrical networks with 15 resistors:

%e   1025,1049,1051,1058,1089,1104,1145,1184,1185,1193,1208,

%e   1212,1219,1248,1254,1337,1382,1403,1526,1527,1529,1530,

%e   1545,1547,1555,1579,1586,1632,1642,1647,1687,1699,1719.

%e Numerators for denominator a(15) = 2153 in electrical networks with 15 resistors:

%e    899, 905, 934, 941, 945, 960, 968, 969,1008,1049,1064,

%e   1095,1102,1104,1128,1137,1143,1147,1164,1182,1207,1296,

%e   1359,1367,1387,1400,1447,1543.

%Y Cf. A180414, A337517, A338601, A339548, A339808, A340726.

%K nonn,hard,more

%O 1,2

%A _Rainer Rosenthal_, Jan 16 2021

%E a(18) from _Hugo Pfoertner_, Apr 11 2021