A324665 - OEIS

%I #9 Mar 11 2019 20:43:37

%S 0,0,2,0,17,17,0,939,6,6,0,8,73,73,7,0,48,445544,10,10,57947,0,30,16,

%T 16,782680,11,11,0,184,2650008,232081,232079,232079,232079,12,0,35,

%U 109811,109809,123,17,15,15,577,0,82,62,62,45,45,104,32,16,16,0,281,279

%N Starting at n, a(n) is the total number of negative positions 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 from zero instead.

%H David Nacin, <a href="/A324665/a324665.png">A324665(n)/A228474(n)</a>

%e For n=2, the points visited are 2,1,-1,-4,0.  As exactly two of these are negative, we have a(2)=2.

%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 sum(1 for i in d['spots'] if i < 0)

%Y Cf. A228474, A324660-A324692

%K nonn

%O 0,3

%A _David Nacin_, Mar 10 2019