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A324679 Starting at n, a(n) is the maximum positive position from which a spot must be revisited on the next move, or zero if no such positions exist, 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. 0

%I

%S 0,0,0,0,0,0,0,3442,0,0,0,27,28,29,0,0,84,2368556,0,0,638385,0,0,0,0,

%T 3642394,0,0,0,464,43807680,2117461,2117462,2117463,2117464,0,0,0,

%U 562491,562492,179,0,0,1,1007,0,104,79,80,0,0,190,0,0,0,0,1107,1108

%N Starting at n, a(n) is the maximum positive position from which a spot must be revisited on the next move, or zero if no such positions exist, 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=11, the points visited are 11, 10, 8, 5, 1, -4, 2, -5, 3, -6, 4, -7, -19, -32, -18, -3, 13, 30, 12, 31, 51, 72, 50, 27, 51, 26, 0. The only position from which we are forced to revisit a spot is 27, which forces a return to 51. Since this is the only time this happens it is also the maximal positive point for which this happens, thus a(11)=27.

%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['stuck'] if i >0 ])

%Y Cf. A228474, A324660-A324692.

%K nonn

%O 0,8

%A _David Nacin_, Mar 10 2019

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Last modified November 18 10:08 EST 2019. Contains 329261 sequences. (Running on oeis4.)