A356201 - OEIS

%I #18 Sep 09 2022 14:50:44

%S 0,4,106,2384,51196,958170,24341911,636875169,14536767750,

%T 285039411789,6322647312660,202105291334913

%N a(n) is the first component x of the distance vector (x,y), x >= y >= 0, between two nodes of an infinite square 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 A356202(n).

%C If more than one solution exists, the one maximizing x and minimizing y is chosen.

%H Hugo Pfoertner, <a href="/A355565/a355565.gp.txt">PARI program for inverse problem</a>, (2022). Finds the grid point [x,y] that leads to the best approximation of a given resistance distance R (ohms) between [0,0] and [x,y].

%e    n                x              y   R(x,y) - n

%e    0                0              0   0

%e    1                4              2  -8.076*10^(-3)

%e    2              106              8   7.349*10^(-6)

%e    3             2384            606   2.206*10^(-8)

%e    4            51196          24881  -7.426*10^(-11)

%e    5           958170         903855   7.396*10^(-16)

%e    6         24341911       18345919  -7.814*10^(-16)

%e    7        636875169      303176603  -3.017*10^(-19)

%e    8      14536767750     7423167971   5.874*10^(-21)

%e    9     285039411789   247828120179  -2.461*10^(-24)

%e   10    6322647312660  6034957650107  -1.048*10^(-26)

%e   11  202105291334913  7948827377158   1.795*10^(-29)

%o (PARI) \\ using the function Rsqlatt(R) from the linked program

%o for (k=0, 11, print1(Rsqlatt(k)[1], ", ")) \\ _Hugo Pfoertner_, Sep 09 2022

%Y Cf. A355565, A355566, A355567, A355953, A355955.

%Y Cf. A356203, A356204 (similar for triangular lattice).

%K nonn,hard,more

%O 0,2

%A _Hugo Pfoertner_, Aug 01 2022

%E a(9)-a(11) from _Hugo Pfoertner_, Aug 22 2022