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 A324678 Starting at n, a(n) is the minimum negative position from which a spot must be revisited on the next move, or zero if no such positions exist, according to the following rules. On the k-th step (k=1,2,3,...) move a distance of k in the direction of zero. If the number landed on has been landed on before, move a distance of k away. 0
 0, 0, 0, 0, 0, 0, 0, -3165, 0, 0, 0, 0, -140, -139, 0, 0, 0, -3072845, 0, 0, -383171, 0, 0, 0, 0, -4869724, 0, 0, 0, -217, -31071367, -1854085, -1854084, -1854083, -1854082, 0, 0, -24, -696919, -696918, -26, -1, 0, 0, -1920, 0, -148, -86, -85, -84, -83, -144 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS Table of n, a(n) for n=0..51. EXAMPLE For n=41, the points visited are 41, 40, 38, 35, 31, 26, 20, 13, 5, -4, 6, -5, 7, -6, 8, -7, 9, -8, 10, -9, 11, -10, 12, -11, -35, -60, -34, -61, -33, -62, -32, -1, -33, 0. The only position from which we are forced to revisit a spot is -1 which forces a return to -33. As this is the only position and it is negative, it is the minimum negative position and thus a(41)=-1. PROG (Python) #Sequences A324660-A324692 generated by manipulating this trip function #spots - positions in order with possible repetition #flee - positions from which we move away from zero with possible repetition #stuck - positions from which we move to a spot already visited with possible repetition def trip(n): stucklist = list() spotsvisited = [n] leavingspots = list() turn = 0 forbidden = {n} while n != 0: turn += 1 sign = n // abs(n) st = sign * turn if n - st not in forbidden: n = n - st else: leavingspots.append(n) if n + st in forbidden: stucklist.append(n) n = n + st spotsvisited.append(n) forbidden.add(n) return {'stuck':stucklist, 'spots':spotsvisited, 'turns':turn, 'flee':leavingspots} def minorzero(x): if x: return min(x) return 0 #Actual sequence def a(n): d=trip(n) return minorzero([i for i in d['stuck'] if i<0]) CROSSREFS Cf. A228474, A324660-A324692. Sequence in context: A151750 A031610 A252636 * A068266 A140350 A309024 Adjacent sequences: A324675 A324676 A324677 * A324679 A324680 A324681 KEYWORD sign AUTHOR David Nacin, Mar 10 2019 STATUS approved

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Last modified May 24 16:32 EDT 2024. Contains 372781 sequences. (Running on oeis4.)