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A324667 Starting at n, a(n) is the maximum negative point visited, or zero if no negative 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. 0

%I

%S 0,0,-1,0,-2,-1,0,-1,-2,-1,0,-3,-2,-1,-1,0,-2,-1,-3,-2,-1,0,-1,-3,-2,

%T -1,-2,-1,0,-6,-1,-1,-3,-2,-1,-1,0,-4,-1,-1,-1,-1,-3,-2,-1,0,-1,-2,-1,

%U -3,-2,-1,-1,-2,-1,0,-1,-1,-6,-1,-4,-3,-2,-1,-1,-1,0,-3

%N Starting at n, a(n) is the maximum negative point visited, or zero if no negative 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 larger of the two negative 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 maxorzero(x):

%o if x:

%o return max(x)

%o return 0

%o #Actual sequence

%o def a(n):

%o d = trip(n)

%o return maxorzero([i for i in d['spots'] if i < 0])

%Y Cf. A228474, A324660-A324692.

%K sign

%O 0,5

%A _David Nacin_, Mar 10 2019

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Last modified September 19 07:08 EDT 2021. Contains 347554 sequences. (Running on oeis4.)