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A324673 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.

%I A324673 #18 Jul 23 2025 16:00:52
%S A324673 0,1,6,3,68,72,6,13205,31,36,10,104,836,836,43,15,570,9518374,57,60,
%T A324673 1548481,21,203,80,87,15466141,71,71,28,2436,118129102,6815959,
%U A324673 6815959,6815959,6815959,86,36,560,2261901,2261901,1091,103,103,103,6831,45,758,499
%N A324673 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 A324673 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 A324673 (Python)
%o A324673 #Sequences A324660-A324692 generated by manipulating this trip function
%o A324673 #spots - positions in order with possible repetition
%o A324673 #flee - positions from which we move away from zero with possible repetition
%o A324673 #stuck - positions from which we move to a spot already visited with possible repetition
%o A324673 def trip(n):
%o A324673     stucklist = list()
%o A324673     spotsvisited = [n]
%o A324673     leavingspots = list()
%o A324673     turn = 0
%o A324673     forbidden = {n}
%o A324673     while n != 0:
%o A324673         turn += 1
%o A324673         sign = n // abs(n)
%o A324673         st = sign * turn
%o A324673         if n - st not in forbidden:
%o A324673             n = n - st
%o A324673         else:
%o A324673             leavingspots.append(n)
%o A324673             if n + st in forbidden:
%o A324673                 stucklist.append(n)
%o A324673             n = n + st
%o A324673         spotsvisited.append(n)
%o A324673         forbidden.add(n)
%o A324673     return {'stuck':stucklist, 'spots':spotsvisited,
%o A324673                 'turns':turn, 'flee':leavingspots}
%o A324673 #Actual sequence
%o A324673 def a(n):
%o A324673     d=trip(n)
%o A324673     return max(d['spots'])-min(d['spots'])
%Y A324673 Cf. A228474, A324660-A324692. Equals A248953 - A248952.
%K A324673 nonn
%O A324673 0,3
%A A324673 _David Nacin_, Mar 10 2019