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%I #16 Mar 14 2019 14:54:38
%S 0,1,6,3,68,72,6,13205,31,36,10,104,836,836,43,15,570,9518374,57,60,
%T 1548481,21,203,80,87,15466141,71,71,28,2436,118129102,6815959,
%U 6815959,6815959,6815959,86,36,560,2261901,2261901,1091,103,103,103,6831,45,758,499
%N Starting at n, a(n) is the length of the smallest interval containing all points 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
%e For n=2, the points visited are 2,1,-1,-4,0. The smallest interval containing these is [-4,2] which has length 6, thus a(2) = 6.
%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(d['spots'])-min(d['spots'])
%Y Cf. A228474, A324660-A324692. Equals A248953 - A248952.
%K nonn
%O 0,3
%A _David Nacin_, Mar 10 2019
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