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.

A344230 Squares visited by a knight (chess piece) moving to the lowest-numbered unvisited square at each step on a semi-infinite chessboard numbered by starting in the lower left and filling in squares in a counterclockwise way moving to the bottom leftmost unnumbered square when the edge of the board is encountered.

Original entry on oeis.org

1, 6, 9, 2, 7, 4, 5, 8, 11, 14, 3, 10, 19, 22, 15, 12, 17, 28, 13, 18, 29, 32, 23, 16, 35, 46, 21, 34, 25, 48, 33, 20, 27, 40, 31, 54, 39, 26, 51, 68, 41, 44, 55, 30, 43, 60, 47, 24, 49, 62, 45, 42, 53, 38, 65, 52, 37, 66, 85, 70, 57, 76, 61, 80, 97, 116, 75, 56, 59, 74, 71, 58, 73, 88, 69, 84, 101, 124, 83, 50, 67, 82, 103, 86, 107, 72, 87, 104, 123, 148, 105, 128, 89, 92, 109, 112, 93, 90, 111, 130, 91, 108, 127, 152, 131, 134, 113, 94, 77, 98, 63, 36
Offset: 1

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Author

Roman Mecholsky, May 12 2021

Keywords

Comments

The sequence is finite and ends at the 111th move, which takes the knight to the square numbered 36 (the leftmost square on the 6th row).
The squares on the board are numbered as follows:
. . . . . . .
. . . . . . .
. . . . . . .
+----+----+----+----+----+----+----+
| 49 | 48 | 47 | 46 | 45 | 44 | 43 | ...
ending +----+----+----+----+----+----+----+
square ---> | 36 | 35 | 34 | 33 | 32 | 31 | 42 | ...
+----+----+----+----+----+----+----+
| 25 | 24 | 23 | 22 | 21 | 30 | 41 | ...
+----+----+----+----+----+----+----+
| 16 | 15 | 14 | 13 | 20 | 29 | 40 | ...
+----+----+----+----+----+----+----+
| 9 | 8 | 7 | 12 | 19 | 28 | 39 | ...
+----+----+----+----+----+----+----+
| 4 | 3 | 6 | 11 | 18 | 27 | 38 | ...
starting +----+----+----+----+----+----+----+
square ---> | 1 | 2 | 5 | 10 | 17 | 26 | 37 | ...
+----+----+----+----+----+----+----+

Crossrefs

Cf. A316667.

Programs

  • Mathematica
    findvalue[{i_, j_}] := If[j > i, (j - 1)^2 + 2 j - i, (i - 1)^2 + j];
    possiblemoves[{i_, j_}, prev_List] :=
      Block[{moves = {{i + 2, j + 1}, {i + 2, j - 1}, {i + 1,
           j + 2}, {i + 1, j - 2}, {i - 1, j + 2}, {i - 1, j - 2}, {i - 2,
            j + 1}, {i - 2, j - 1}}, list},
       list = DeleteCases[moves, {x_, y_} /; x < 1 || y < 1];
       Complement[list, Intersection[list, prev]]];
    findnextmove =
      Block[{listofmoves = #, nextmove, poss},
        pos = possiblemoves[listofmoves[[-1]], listofmoves];
        If[Length[pos] > 0,
         nextmove = Sort[({findvalue[#], #} &) /@ pos][[1, 2]];
         AppendTo[listofmoves, nextmove], listofmoves]] &;
    findvalue /@ FixedPoint[findnextmove, {{1, 1}}]