%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