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A324663 Starting at n, a(n) is the number of moves made away from zero 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 from zero instead.

%I A324663 #8 Mar 11 2019 20:43:21
%S A324663 0,0,1,0,9,10,0,740,2,3,0,7,48,49,2,0,39,348242,3,4,59273,0,12,5,6,
%T A324663 523146,3,4,0,177,3533234,241226,241225,241226,241227,3,0,28,101615,
%U A324663 101614,93,5,4,5,420,0,49,34,35,23,24,84,13,4,5,0,262,261,260,221950
%N A324663 Starting at n, a(n) is the number of moves made away from zero 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 from zero instead.
%H A324663 David Nacin, <a href="/A324663/a324663.png">A324663(n)/A228474(n)</a>
%e A324663 For n=2, the points visited are 2,1,-1,-4,0 with all moves being towards zero from the current position except for the move from -1 to -4, hence a(2) = 1.
%o A324663 (Python)
%o A324663 #Sequences A324660-A324692 generated by manipulating this trip function
%o A324663 #spots - positions in order with possible repetition
%o A324663 #flee - positions from which we move away from zero with possible repetition
%o A324663 #stuck - positions from which we move to a spot already visited with possible repetition
%o A324663 def trip(n):
%o A324663     stucklist = list()
%o A324663     spotsvisited = [n]
%o A324663     leavingspots = list()
%o A324663     turn = 0
%o A324663     forbidden = {n}
%o A324663     while n != 0:
%o A324663         turn += 1
%o A324663         sign = n // abs(n)
%o A324663         st = sign * turn
%o A324663         if n - st not in forbidden:
%o A324663             n = n - st
%o A324663         else:
%o A324663             leavingspots.append(n)
%o A324663             if n + st in forbidden:
%o A324663                 stucklist.append(n)
%o A324663             n = n + st
%o A324663         spotsvisited.append(n)
%o A324663         forbidden.add(n)
%o A324663     return {'stuck':stucklist, 'spots':spotsvisited,
%o A324663                 'turns':turn, 'flee':leavingspots}
%o A324663 #Actual sequence
%o A324663 def a(n):
%o A324663     d = trip(n)
%o A324663     return len(d['flee'])
%Y A324663 Cf. A228474, A324660-A324692
%K A324663 nonn
%O A324663 0,5
%A A324663 _David Nacin_, Mar 10 2019