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 A324680 Starting at n, a(n) is the largest distance from zero among all positions 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. 2
 0, 0, 0, 0, 0, 0, 0, 3442, 0, 0, 0, 27, 140, 139, 0, 0, 84, 3072845, 0, 0, 638385, 0, 0, 0, 0, 4869724, 0, 0, 0, 464, 43807680, 2117461, 2117462, 2117463, 2117464, 0, 0, 24, 696919, 696918, 179, 1, 0, 1, 1920, 0, 148, 86, 85, 84, 83, 190, 63, 0, 0, 0, 1107 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS David Nacin, A324680 David Nacin, A324680(n)/A228474(n) EXAMPLE For n=11, the points visited are 11, 10, 8, 5, 1, -4, 2, -5, 3, -6, 4, -7, -19, -32, -18, -3, 13, 30, 12, 31, 51, 72, 50, 27, 51, 26, 0.  The only position from which we are forced to revisit a spot is 27, which forces a return to 51. Since this is the only time this happens it is also has the largest distance from zero, thus a(11)=27. 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 maxorzero(x):     if x:         return max(x)     return 0 #Actual sequence def a(n):     d=trip(n)     return maxorzero([abs(i) for i in d['stuck']]) CROSSREFS Cf. A228474, A324660-A324692. Sequence in context: A254093 A254086 A324679 * A273341 A107537 A260500 Adjacent sequences:  A324677 A324678 A324679 * A324681 A324682 A324683 KEYWORD nonn AUTHOR David Nacin, Mar 10 2019 STATUS approved

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Last modified May 26 04:43 EDT 2022. Contains 354074 sequences. (Running on oeis4.)