cp's OEIS Frontend

A324660 Starting at n, a(n) is the total number of moves made to the right 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 A324660 #17 Mar 11 2019 20:31:40
%S A324660 0,0,1,0,10,11,0,861,4,5,0,11,59,60,5,0,57,390898,7,8,66444,0,22,11,
%T A324660 12,610392,8,9,0,211,4434560,266001,266000,266001,266002,9,0,43,
%U A324660 106674,106673,120,12,11,12,495,0,67,50,51,36,37,100,25,12,13,0,317,316
%N A324660 Starting at n, a(n) is the total number of moves made to the right 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.
%e A324660 For n=2, the points visited are 2,1,-1,-4,0 with the move from -4 to 0 being the only one to the right, hence a(2)=1.
%o A324660 (Python)
%o A324660 #Sequences A324660-A324692 generated by manipulating this trip function
%o A324660 #spots - positions in order with possible repetition
%o A324660 #flee - positions from which we move away from zero with possible repetition
%o A324660 #stuck - positions from which we move to a spot already visited with possible repetition
%o A324660 def trip(n):
%o A324660     stucklist = list()
%o A324660     spotsvisited = [n]
%o A324660     leavingspots = list()
%o A324660     turn = 0
%o A324660     forbidden = {n}
%o A324660     while n != 0:
%o A324660         turn += 1
%o A324660         sign = n // abs(n)
%o A324660         st = sign * turn
%o A324660         if n - st not in forbidden:
%o A324660             n = n - st
%o A324660         else:
%o A324660             leavingspots.append(n)
%o A324660             if n + st in forbidden:
%o A324660                 stucklist.append(n)
%o A324660             n = n + st
%o A324660         spotsvisited.append(n)
%o A324660         forbidden.add(n)
%o A324660     return {'stuck':stucklist, 'spots':spotsvisited,
%o A324660                 'turns':turn, 'flee':leavingspots}
%o A324660 #Actual sequence
%o A324660 def a(n):
%o A324660     d=trip(n)
%o A324660     return sum(1 for i in range(d['turns']) if d['spots'][i+1] > d['spots'][i])
%Y A324660 Cf. A228474, A324660-A324692
%K A324660 nonn
%O A324660 0,5
%A A324660 _David Nacin_, Mar 10 2019