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A340708 Maximum denominator of resistances obtained by an electrical network with n unit resistors.

%I A340708 #30 Apr 19 2021 10:30:22
%S A340708 1,2,3,5,8,13,24,40,69,130,231,408,689,1272,2153,3960,6993,12560
%N A340708 Maximum denominator of resistances obtained by an electrical network with n unit resistors.
%C A340708 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 A340708 Also the maximum numerator of these electrical networks for small n.
%C A340708 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 A340708 The asymmetry is illustrated by the example a(15) = 2153.
%C A340708 The author conjectures that this asymmetry will increase with n, and eventually the maxima will differ.
%C A340708 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 A340708 <a href="/index/Res#resistances">Index to sequences related to resistances</a>.
%e A340708 Denominators for numerator a(15) = 2153 in electrical networks with 15 resistors:
%e A340708   1025,1049,1051,1058,1089,1104,1145,1184,1185,1193,1208,
%e A340708   1212,1219,1248,1254,1337,1382,1403,1526,1527,1529,1530,
%e A340708   1545,1547,1555,1579,1586,1632,1642,1647,1687,1699,1719.
%e A340708 Numerators for denominator a(15) = 2153 in electrical networks with 15 resistors:
%e A340708    899, 905, 934, 941, 945, 960, 968, 969,1008,1049,1064,
%e A340708   1095,1102,1104,1128,1137,1143,1147,1164,1182,1207,1296,
%e A340708   1359,1367,1387,1400,1447,1543.
%Y A340708 Cf. A180414, A337517, A338601, A339548, A339808, A340726.
%K A340708 nonn,hard,more
%O A340708 1,2
%A A340708 _Rainer Rosenthal_, Jan 16 2021
%E A340708 a(18) from _Hugo Pfoertner_, Apr 11 2021