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%I #8 Mar 11 2019 20:43:21
%S 0,0,1,0,9,10,0,740,2,3,0,7,48,49,2,0,39,348242,3,4,59273,0,12,5,6,
%T 523146,3,4,0,177,3533234,241226,241225,241226,241227,3,0,28,101615,
%U 101614,93,5,4,5,420,0,49,34,35,23,24,84,13,4,5,0,262,261,260,221950
%N Starting at n, a(n) is the number of moves made 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 from zero instead.
%H David Nacin, <a href="/A324663/a324663.png">A324663(n)/A228474(n)</a>
%e For n=2, the points visited are 2,1,-1,-4,0 with all moves being towards zero from the current position except for the move from -1 to -4, 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 len(d['flee'])
%Y Cf. A228474, A324660-A324692
%K nonn
%O 0,5
%A _David Nacin_, Mar 10 2019
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