cp's OEIS Frontend

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.

%I A324680 #6 Mar 11 2019 20:45:44
%S A324680 0,0,0,0,0,0,0,3442,0,0,0,27,140,139,0,0,84,3072845,0,0,638385,0,0,0,
%T A324680 0,4869724,0,0,0,464,43807680,2117461,2117462,2117463,2117464,0,0,24,
%U A324680 696919,696918,179,1,0,1,1920,0,148,86,85,84,83,190,63,0,0,0,1107
%N 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.
%H A324680 David Nacin, <a href="/A324680/a324680.png">A324680</a>
%H A324680 David Nacin, <a href="/A324680/a324680_1.png">A324680(n)/A228474(n)</a>
%e A324680 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.
%o A324680 (Python)
%o A324680 #Sequences A324660-A324692 generated by manipulating this trip function
%o A324680 #spots - positions in order with possible repetition
%o A324680 #flee - positions from which we move away from zero with possible repetition
%o A324680 #stuck - positions from which we move to a spot already visited with possible repetition
%o A324680 def trip(n):
%o A324680     stucklist = list()
%o A324680     spotsvisited = [n]
%o A324680     leavingspots = list()
%o A324680     turn = 0
%o A324680     forbidden = {n}
%o A324680     while n != 0:
%o A324680         turn += 1
%o A324680         sign = n // abs(n)
%o A324680         st = sign * turn
%o A324680         if n - st not in forbidden:
%o A324680             n = n - st
%o A324680         else:
%o A324680             leavingspots.append(n)
%o A324680             if n + st in forbidden:
%o A324680                 stucklist.append(n)
%o A324680             n = n + st
%o A324680         spotsvisited.append(n)
%o A324680         forbidden.add(n)
%o A324680     return {'stuck':stucklist, 'spots':spotsvisited,
%o A324680                 'turns':turn, 'flee':leavingspots}
%o A324680 def maxorzero(x):
%o A324680     if x:
%o A324680         return max(x)
%o A324680     return 0
%o A324680 #Actual sequence
%o A324680 def a(n):
%o A324680     d=trip(n)
%o A324680     return maxorzero([abs(i) for i in d['stuck']])
%Y A324680 Cf. A228474, A324660-A324692.
%K A324680 nonn
%O A324680 0,8
%A A324680 _David Nacin_, Mar 10 2019