A324668 - OEIS

%I #7 Mar 11 2019 20:44:01

%S 0,1,1,2,1,1,3,1,2,1,4,1,1,1,4,5,1,1,3,1,1,6,1,2,1,1,5,1,7,1,1,2,3,1,

%T 1,7,8,1,1,2,3,5,6,1,1,9,1,2,1,4,1,1,7,8,1,10,1,2,3,1,2,1,1,1,9,10,11,

%U 1,1,1,4,5,6,7,1,9,1,1,12,1,2,3,4,5,6,1

%N Starting at n, a(n) is the minimum positive point visited, or zero if no positive points are 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.

%e For n=2, the points visited are 2,1,-1,-4,0.  As 1 is the smaller of the two positive values, a(2) = 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 def minorzero(x):

%o     if x:

%o         return min(x)

%o     return 0

%o #Actual sequence

%o def a(n):

%o     d = trip(n)

%o     return minorzero([i for i in d['spots'] if i > 0])

%Y Cf. A228474, A324660-A324692.

%K nonn

%O 0,4

%A _David Nacin_, Mar 10 2019