cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

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

Views

Author

Hugo Pfoertner, Aug 13 2022

Keywords

Examples

			  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)
		

Crossrefs

Cf. A356201, A356202 (similar for square lattice).

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

Views

Author

Hugo Pfoertner, Aug 01 2022

Keywords

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)
		

Crossrefs

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
Showing 1-2 of 2 results.