cp's OEIS Frontend

A324661 Starting at n, a(n) is the total number of moves made to the left 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 A324661 #11 Mar 11 2019 20:32:02
%S A324661 0,1,3,2,14,15,3,864,8,9,4,15,64,65,10,5,62,390904,13,14,66452,6,29,
%T A324661 18,19,610401,15,16,7,218,4434563,266008,266007,266008,266009,17,8,51,
%U A324661 106681,106680,128,21,20,21,505,9,77,60,61,46,47,110,35,22,23,10,327
%N A324661 Starting at n, a(n) is the total number of moves made to the left 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 A324661 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 the only ones to the left, hence a(2)=3.
%o A324661 (Python)
%o A324661 #Sequences A324660-A324692 generated by manipulating this trip function
%o A324661 #spots - positions in order with possible repetition
%o A324661 #flee - positions from which we move away from zero with possible repetition
%o A324661 #stuck - positions from which we move to a spot already visited with possible repetition
%o A324661 def trip(n):
%o A324661     stucklist = list()
%o A324661     spotsvisited = [n]
%o A324661     leavingspots = list()
%o A324661     turn = 0
%o A324661     forbidden = {n}
%o A324661     while n != 0:
%o A324661         turn += 1
%o A324661         sign = n // abs(n)
%o A324661         st = sign * turn
%o A324661         if n - st not in forbidden:
%o A324661             n = n - st
%o A324661         else:
%o A324661             leavingspots.append(n)
%o A324661             if n + st in forbidden:
%o A324661                 stucklist.append(n)
%o A324661             n = n + st
%o A324661         spotsvisited.append(n)
%o A324661         forbidden.add(n)
%o A324661     return {'stuck':stucklist, 'spots':spotsvisited,
%o A324661                 'turns':turn, 'flee':leavingspots}
%o A324661 #Actual sequence
%o A324661 def a(n):
%o A324661     d = trip(n)
%o A324661     return sum(1 for i in range(d['turns']) if d['spots'][i+1] < d['spots'][i])
%Y A324661 Cf. A228474, A324660-A324692. Equals (A228474-A324660).
%K A324661 nonn
%O A324661 0,3
%A A324661 _David Nacin_, Mar 10 2019