cp's OEIS Frontend

A324662 Starting at n, a(n) is the difference of the number of left moves and the number of right moves 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.

%I A324662 #11 Mar 11 2019 20:43:13
%S A324662 0,1,2,2,4,4,3,3,4,4,4,4,5,5,5,5,5,6,6,6,8,6,7,7,7,9,7,7,7,7,3,7,7,7,
%T A324662 7,8,8,8,7,7,8,9,9,9,10,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
%U A324662 10,10,10,10,11,11,11,12,12,12,12,12,12,12,12,12
%N A324662 Starting at n, a(n) is the difference of the number of left moves and the number of right moves 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 A324662 David Nacin, <a href="/A324662/a324662.png">a(n)/sqrt{n}</a>
%e A324662 For n=2, the points visited are 2,1,-1,-4,0 with the moves from 2 to 1, 1 to -1, and -1 to -4 being to the left, and the move from -4 to 0 being to the right, hence a(2) = 3 - 1 = 2.
%o A324662 (Python)
%o A324662 #Sequences A324660-A324692 generated by manipulating this trip function
%o A324662 #spots - positions in order with possible repetition
%o A324662 #flee - positions from which we move away from zero with possible repetition
%o A324662 #stuck - positions from which we move to a spot already visited with possible repetition
%o A324662 def trip(n):
%o A324662     stucklist = list()
%o A324662     spotsvisited = [n]
%o A324662     leavingspots = list()
%o A324662     turn = 0
%o A324662     forbidden = {n}
%o A324662     while n != 0:
%o A324662         turn += 1
%o A324662         sign = n // abs(n)
%o A324662         st = sign * turn
%o A324662         if n - st not in forbidden:
%o A324662             n = n - st
%o A324662         else:
%o A324662             leavingspots.append(n)
%o A324662             if n + st in forbidden:
%o A324662                 stucklist.append(n)
%o A324662             n = n + st
%o A324662         spotsvisited.append(n)
%o A324662         forbidden.add(n)
%o A324662     return {'stuck':stucklist, 'spots':spotsvisited,
%o A324662                 'turns':turn, 'flee':leavingspots}
%o A324662 def sgn(x):
%o A324662     return x//abs(x)
%o A324662 #Actual sequence
%o A324662 def a(n):
%o A324662     d = trip(n)
%o A324662     return sum(sgn(d['spots'][i] - d['spots'][i+1]) for i in range(d['turns']))
%Y A324662 Cf. A228474, A324660-A324692. Equals (A324661-A324660).
%K A324662 nonn
%O A324662 0,3
%A A324662 _David Nacin_, Mar 10 2019