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 A352731 On a diagonally numbered square grid, with labels starting at 1, this is the number of the last cell that a (1,n) leaper reaches before getting trapped when moving to the lowest available unvisited square, or -1 if it never gets trapped. 2
 -1, 1378, -1, 595, 66, 36, 153, 758, 1185, 78, 1732, 171, 2510, 2094, 1407, 253, 630, 210, 780, 2385, 1326, 300, 1225, 990, 2800, 406, 3267, 4333, 4124, 528, 4309, 741, 5951, 666, 2701, 903, 30418, 820, 3321, 1081, 4186, 990, 8299, 2775, 4560, 1176, 4753, 39951, 5778 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A (1,2) leaper is a chess knight. (1,1) and (1,3) leapers both never get trapped. This is understandable for the (1,1) leaper but not so much for the (1,3) which does get trapped on the spirally numbered board (see A323471). Once the (1,3) leaper reaches 39 it then performs the same set of 4 moves repeatedly, meaning that it never gets trapped. LINKS Table of n, a(n) for n=1..49. PROG (Python) # reformatted by R. J. Mathar, 2023-03-29 class A352731(): def __init__(self, n) : self.n = n self.KM=[(n, 1), (1, n), (-1, n), (-n, 1), (-n, -1), (-1, -n), (1, -n), (n, -1)] @staticmethod def _idx(loc): i, j = loc return (i+j-1)*(i+j-2)//2 + j def _next_move(self, loc, visited): i, j = loc moves = [(i+io, j+jo) for io, jo in self.KM if i+io>0 and j+jo>0] available = [m for m in moves if m not in visited] return min(available, default=None, key=lambda x: A352731._idx(x)) def _aseq(self): locs = [[], []] loc, s, turn, alst = [(1, 1), (1, 1)], {(1, 1)}, 0,  m = self._next_move(loc[turn], s) while m != None: loc[turn], s, turn, alst = m, s|{m}, 0 , alst + [A352731._idx(m)] locs[turn] += [loc[turn]] m = self._next_move(loc[turn], s) if len(s)%100000 == 0: print(self.n, '{steps} moves in'.format(steps = len(s))) return alst def at(self, n) : if n == 1 or n == 3: return -1 else: return self._aseq()[-1] for n in range(1, 40): a352731 = A352731(n) print(a352731.at(n)) CROSSREFS Cf. A323469, A323471, A352730. Sequence in context: A345515 A345768 A323815 * A307422 A256627 A260368 Adjacent sequences: A352728 A352729 A352730 * A352732 A352733 A352734 KEYWORD sign AUTHOR Andrew Smith, Mar 30 2022 STATUS approved

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Last modified May 27 23:25 EDT 2023. Contains 362992 sequences. (Running on oeis4.)