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%I #8 Mar 11 2019 20:43:31
%S 0,0,1,0,3,1,0,5,4,1,0,7,6,1,4,0,7,8,7,1,2,0,5,4,1,2,7,1,0,13,2,1,10,
%T 1,1,7,0,5,1,3,2,1,10,1,2,0,17,16,1,14,1,2,11,10,1,0,1,1,17,1,15,1,1,
%U 1,11,10,0,4,1,2,1,1,1,15,1,13,1,1,0,2,1,1
%N Starting at n, a(n) is the smallest distance from zero for which the next move is a step away from zero, or zero if no such move is ever made, 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 David Nacin, <a href="/A324664/a324664.png">A324664(n)/sqrt(n)</a>
%e 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. Thus the closest distance to zero from which a move is made away from zero is a(2) = 1.
%o (Python)
%o #Sequences A324660-A324692 generated by manipulating this trip function
%o #spots - positions in order with possible repetition
%o #flee - positions from which we move away from zero with possible repetition
%o #stuck - positions from which we move to a spot already visited with possible repetition
%o def trip(n):
%o stucklist = list()
%o spotsvisited = [n]
%o leavingspots = list()
%o turn = 0
%o forbidden = {n}
%o while n != 0:
%o turn += 1
%o sign = n // abs(n)
%o st = sign * turn
%o if n - st not in forbidden:
%o n = n - st
%o else:
%o leavingspots.append(n)
%o if n + st in forbidden:
%o stucklist.append(n)
%o n = n + st
%o spotsvisited.append(n)
%o forbidden.add(n)
%o return {'stuck':stucklist, 'spots':spotsvisited,
%o 'turns':turn, 'flee':leavingspots}
%o def minorzero(x):
%o if x:
%o return min(x)
%o return 0
%o #Actual sequence
%o def a(n):
%o d = trip(n)
%o return minorzero([abs(i) for i in d['flee']])
%Y Cf. A228474, A324660-A324692
%K nonn
%O 0,5
%A _David Nacin_, Mar 10 2019
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