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Starting at n, a(n) is the distance from zero of the farthest point 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.
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%I #14 Mar 14 2019 14:54:12

%S 0,1,4,3,47,46,6,6843,23,22,10,72,471,470,29,15,352,4843985,39,38,

%T 891114,21,102,57,56,7856204,45,44,28,1700,61960674,3702823,3702824,

%U 3702825,3702826,51,36,370,1213998,1213997,596,62,61,60,3855,45,417,260,261,237

%N Starting at n, a(n) is the distance from zero of the farthest point 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.

%H David Nacin, <a href="/A324671/a324671.png">A324671</a>

%H David Nacin, <a href="/A324671/a324671_1.png">A324671(n)/A228474(n)</a>

%e For n=2, the points visited are 2,1,-1,-4,0. Of those the one farthest from zero is -4 with a distance of 4, hence a(2) = 4.

%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 max(abs(i) for i in d['spots'])

%Y Cf. A228474, A324660-A324692. Equals max(A248953, -A248952).

%K nonn

%O 0,3

%A _David Nacin_, Mar 10 2019