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).

0, 4, 106, 2384, 51196, 958170, 24341911, 636875169, 14536767750, 285039411789, 6322647312660, 202105291334913

Offset: 0

Author

Hugo Pfoertner, Aug 01 2022

Keywords

• nonn
• hard
• more

Comments

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

Examples

			   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)
		

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].

Crossrefs

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

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

Programs

PARI

\\ using the function Rsqlatt(R) from the linked program
for (k=0, 11, print1(Rsqlatt(k)[1], ", ")) \\ Hugo Pfoertner, Sep 09 2022

Extensions

a(9)-a(11) from Hugo Pfoertner, Aug 22 2022