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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).
4
0, 4, 106, 2384, 51196, 958170, 24341911, 636875169, 14536767750, 285039411789, 6322647312660, 202105291334913
OFFSET
0,2
COMMENTS
If more than one solution exists, the one maximizing x and minimizing y is chosen.
LINKS
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].
EXAMPLE
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)
PROG
(PARI) \\ using the function Rsqlatt(R) from the linked program
for (k=0, 11, print1(Rsqlatt(k)[1], ", ")) \\ Hugo Pfoertner, Sep 09 2022
CROSSREFS
Cf. A356203, A356204 (similar for triangular lattice).
Sequence in context: A203313 A087178 A104595 * A222930 A221187 A220531
KEYWORD
nonn,hard,more
AUTHOR
Hugo Pfoertner, Aug 01 2022
EXTENSIONS
a(9)-a(11) from Hugo Pfoertner, Aug 22 2022
STATUS
approved