A324275
Numbers k for which A324274(k) is 0, i.e., starting squares in A324274 that yield a path of infinite length.
Original entry on oeis.org
2, 9, 14, 27, 34, 53, 64, 89, 102, 133, 150, 187, 206, 249, 272, 321, 346, 401, 430, 491, 522, 589, 624, 697, 734, 813, 854, 939, 982, 1073, 1120, 1217, 1266, 1369, 1422, 1531, 1586, 1701, 1760, 1881, 1942, 2069, 2134, 2267, 2334, 2473
Offset: 1
A324273
Squares visited by a single pawn move for an even square and a double pawn move for an odd square on a diagonally numbered board and moving to the lowest available unvisited square of different parity at each step.
Original entry on oeis.org
1, 4, 7, 2, 5, 12, 17, 8, 13, 6, 3, 10, 15, 26, 19, 32, 25, 14, 9, 18
Offset: 1
Square 1 is odd. Hence the next square should be the lowest even square a double move away from 1, which is square 4. Next, there is only a single option to move in a single move to an odd square, namely at square 7. Etc.
A307344
Cells visited by a single pawn move for an even cell and a double pawn move for an odd cell on a numbered 3D grid and moving to the lowest available unvisited cell of different parity at each step.
Original entry on oeis.org
1, 10, 19, 48, 27, 76, 51, 20, 33, 8, 15, 4, 9, 34, 53, 108, 77, 28, 13, 2, 5, 30, 47, 18, 31, 6, 3, 12, 23, 72, 49, 102, 71, 22, 11, 36, 21, 70, 101, 186, 131, 252, 193, 106, 75, 26, 43, 16
Offset: 1
1: [0, 0, 0] is an odd cell, hence a double move is required. Since 5: [0, 0, 2] and 7: [0, 2, 0] are also odd, 10: [2, 0, 0] is the only valid move.
The sequence ends at 16: [1, 1, 1]. A single move is required, which limits the possible destination cells to:
6: [0, 1, 1], even;
8: [1, 0, 1], even;
9: [1, 1, 0], already visited;
27: [1, 1, 2], already visited;
28: [1, 2, 1], even;
31: [2, 1, 1], already visited;
Showing 1-3 of 3 results.
Comments