A324684 - OEIS

%I #5 Mar 11 2019 20:46:01

%S 0,0,0,0,0,0,0,31,0,0,0,1,1,1,0,0,3,25871,0,0,6154,0,0,0,0,30429,0,0,

%T 0,9,422464,25055,25055,25056,25057,0,0,0,9685,9685,5,0,0,1,20,0,3,1,

%U 1,0,0,5,0,0,0,0,17,17,17,15244,15244,15245,15246,15247,1,0

%N Starting at n, a(n) is the number of times we move from a positive spot to a spot we have already 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 For n=43, the points visited are 43, 42, 40, 37, 33, 28, 22, 15, 7, -2, 8, -3, 9, -4, 10, -5, 11, -6, 12, -7, 13, -8, 14, -9, -33, -58, -32, -59, -31, -60, -30, 1, 33, 0.  The only time we revisit a spot is when we move from 1 to 33.  As this only occurs for one positive number, a(43)=1.

%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['stuck'] if i > 0)

%Y Cf. A228474, A324660-A324692.

%K nonn

%O 0,8

%A _David Nacin_, Mar 10 2019