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).
Original entry on oeis.org
0, 43, 9615, 2299822, 507491696, 118805048562, 25315296119626, 5959615271620724
Offset: 0
n x y R(x,y) - n
0 0 0 0
1 43 18 5.033*10^(-6)
2 9615 2536 1.848*10^(-10)
3 2299822 1136101 -3.120*10^(-14)
4 507491696 119227930 5.751*10^(-19)
5 118805048562 33636581266 5.618*10^(-23)
6 25315296119626 1774960492720 8.406*10^(-29)
7 5959615271620724 685318499093455 2.526*10^(-32)
A356201
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).
Original entry on oeis.org
0, 4, 106, 2384, 51196, 958170, 24341911, 636875169, 14536767750, 285039411789, 6322647312660, 202105291334913
Offset: 0
n x y R(x,y) - n
0 0 0 0
1 4 2 -8.076*10^(-3)
2 106 8 7.349*10^(-6)
3 2384 606 2.206*10^(-8)
4 51196 24881 -7.426*10^(-11)
5 958170 903855 7.396*10^(-16)
6 24341911 18345919 -7.814*10^(-16)
7 636875169 303176603 -3.017*10^(-19)
8 14536767750 7423167971 5.874*10^(-21)
9 285039411789 247828120179 -2.461*10^(-24)
10 6322647312660 6034957650107 -1.048*10^(-26)
11 202105291334913 7948827377158 1.795*10^(-29)
- Hugo Pfoertner, PARI program for inverse problem, (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].
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\\ using the function Rsqlatt(R) from the linked program
for (k=0, 11, print1(Rsqlatt(k)[1], ", ")) \\ Hugo Pfoertner, Sep 09 2022
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