%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