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A356203 a(n) is the first component x of the distance vector (x,y) in an oblique 120-degree coordinate system, 0 <= y <= x, between two nodes of an infinite triangular lattice of one-ohm resistors, such that the resistance R between the two nodes is as close as possible to n ohms, i.e., abs(R - n) is minimized. y is A356204(n).

%I A356203 #9 Aug 27 2022 13:47:41
%S A356203 0,43,9615,2299822,507491696,118805048562,25315296119626,
%T A356203 5959615271620724
%N A356203 a(n) is the first component x of the distance vector (x,y) in an oblique 120-degree coordinate system, 0 <= y <= x, between two nodes of an infinite triangular lattice of one-ohm resistors, such that the resistance R between the two nodes is as close as possible to n ohms, i.e., abs(R - n) is minimized. y is A356204(n).
%e A356203   n                   x                  y    R(x,y) - n
%e A356203   0                   0                  0    0
%e A356203   1                  43                 18    5.033*10^(-6)
%e A356203   2                9615               2536    1.848*10^(-10)
%e A356203   3             2299822            1136101   -3.120*10^(-14)
%e A356203   4           507491696          119227930    5.751*10^(-19)
%e A356203   5        118805048562        33636581266    5.618*10^(-23)
%e A356203   6      25315296119626      1774960492720    8.406*10^(-29)
%e A356203   7    5959615271620724    685318499093455    2.526*10^(-32)
%Y A356203 Cf. A355585, A355586, A355587, A355588, A355589, A355954.
%Y A356203 Cf. A356201, A356202 (similar for square lattice).
%K A356203 nonn,hard,more
%O A356203 0,2
%A A356203 _Hugo Pfoertner_, Aug 13 2022