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%I #8 Mar 11 2019 20:43:56
%S 0,0,-1,0,-2,-1,0,-1,-2,-1,0,-3,-2,-1,-1,0,-2,-1,-3,-2,-1,0,-1,-3,-2,
%T -1,-2,-1,0,-6,-1,-1,-3,-2,-1,-1,0,-4,-1,-1,-1,-1,-3,-2,-1,0,-1,-2,-1,
%U -3,-2,-1,-1,-2,-1,0,-1,-1,-6,-1,-4,-3,-2,-1,-1,-1,0,-3
%N Starting at n, a(n) is the maximum negative point visited, or zero if no negative points are visited, 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.
%e For n=2, the points visited are 2,1,-1,-4,0. As -1 is the larger of the two negative values, 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 maxorzero(x):
%o if x:
%o return max(x)
%o return 0
%o #Actual sequence
%o def a(n):
%o d = trip(n)
%o return maxorzero([i for i in d['spots'] if i < 0])
%Y Cf. A228474, A324660-A324692.
%K sign
%O 0,5
%A _David Nacin_, Mar 10 2019
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