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Starting at n, a(n) is the number of times we move from a negative position to a spot we have already 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.
1

%I #5 Mar 11 2019 20:45:54

%S 0,0,0,0,0,0,0,52,0,0,0,0,6,6,0,0,0,33300,0,0,4302,0,0,0,0,58682,0,0,

%T 0,6,154594,18830,18829,18829,18829,0,0,2,10283,10282,3,1,0,0,29,0,5,

%U 3,3,3,3,5,2,0,0,0,9,9,9,21706,21705,21705,21705,21705,1,0

%N Starting at n, a(n) is the number of times we move from a negative position to a spot we have already 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.

%e For n=41, the points visited are 41, 40, 38, 35, 31, 26, 20, 13, 5, -4, 6, -5, 7, -6, 8, -7, 9, -8, 10, -9, 11, -10, 12, -11, -35, -60, -34, -61, -33, -62, -32, -1, -33, 0. The only time we revisit a spot is when we move from -1 to -33. As this only occurs for one negative number, a(41)=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 #Actual sequence

%o def a(n):

%o d = trip(n)

%o return sum(1 for i in d['stuck'] if i < 0)

%Y Cf. A228474, A324660-A324692.

%K nonn

%O 0,8

%A _David Nacin_, Mar 10 2019