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Starting at n, a(n) is the total number of moves made to the right 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.
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%I #17 Mar 11 2019 20:31:40

%S 0,0,1,0,10,11,0,861,4,5,0,11,59,60,5,0,57,390898,7,8,66444,0,22,11,

%T 12,610392,8,9,0,211,4434560,266001,266000,266001,266002,9,0,43,

%U 106674,106673,120,12,11,12,495,0,67,50,51,36,37,100,25,12,13,0,317,316

%N Starting at n, a(n) is the total number of moves made to the right 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 with the move from -4 to 0 being the only one to the right, hence 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 #Actual sequence

%o def a(n):

%o d=trip(n)

%o return sum(1 for i in range(d['turns']) if d['spots'][i+1] > d['spots'][i])

%Y Cf. A228474, A324660-A324692

%K nonn

%O 0,5

%A _David Nacin_, Mar 10 2019