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%I #14 Jan 10 2023 10:55:04
%S 0,0,-1,0,-1,1,0,-1,-1,1,0,-1,-1,1,-1,0,1,0,-1,1,1,0,-1,-1,1,0,-1,1,0,
%T -1,-1,-1,-1,1,1,-1,0,-1,-1,-1,-1,-1,-1,1,1,0,-1,-1,1,-1,1,1,-1,-1,1,
%U 0,-1,-1,-1,-1,-1,1,1,1,-1,-1,0,-1,1,0,-1,-1,-1
%N Starting at n, a(n) is the sign of the closest nonzero point to zero visited for which the next move is a step 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. In the case of a tie, or if the set of points is empty, we set a(n)=0.
%e For n=9, the points visited are 9, 8, 6, 3, -1, 4, -2, 5, -3, -12, -22, -11, 1, 14, 0. The three times moves are made away from zero happen at -3, -12 and 1. The closest of these is to zero is 1 and thus a(9) = sgn(1) = 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 sgn(x):
%o if x:
%o return x//abs(x)
%o return 0
%o def maxorzero(x):
%o if x:
%o return max(x)
%o return 0
%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 neg=maxorzero([i for i in d['flee'] if i < 0])
%o pos=minorzero([i for i in d['flee'] if i > 0])
%o if neg and not pos:
%o return -1
%o return -sgn(neg+pos)
%Y Cf. A228474, A324660-A324692.
%K sign
%O 0,1
%A _David Nacin_, Mar 10 2019
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