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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
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, 3642394, 0, 0, 0, 464, 43807680, 2117461, 2117462, 2117463, 2117464, 0, 0, 0, 562491, 562492, 179, 0, 0, 1, 1007, 0, 104, 79, 80, 0, 0, 190, 0, 0, 0, 0, 1107, 1108 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Table of n, a(n) for n=0..57.

EXAMPLE

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.

PROG

(Python)

#Sequences A324660-A324692 generated by manipulating this trip function

#spots - positions in order with possible repetition

#flee - positions from which we move away from zero with possible repetition

#stuck - positions from which we move to a spot already visited with possible repetition

def trip(n):

    stucklist = list()

    spotsvisited = [n]

    leavingspots = list()

    turn = 0

    forbidden = {n}

    while n != 0:

        turn += 1

        sign = n // abs(n)

        st = sign * turn

        if n - st not in forbidden:

            n = n - st

        else:

            leavingspots.append(n)

            if n + st in forbidden:

                stucklist.append(n)

            n = n + st

        spotsvisited.append(n)

        forbidden.add(n)

    return {'stuck':stucklist, 'spots':spotsvisited,

                'turns':turn, 'flee':leavingspots}

def maxorzero(x):

    if x:

        return max(x)

    return 0

#Actual sequence

def a(n):

    d=trip(n)

    return maxorzero([i for i in d['stuck'] if i >0 ])

CROSSREFS

Cf. A228474, A324660-A324692.

Sequence in context: A031824 A254093 A254086 * A324680 A273341 A107537

Adjacent sequences:  A324676 A324677 A324678 * A324680 A324681 A324682

KEYWORD

nonn

AUTHOR

David Nacin, Mar 10 2019

STATUS

approved

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Last modified October 21 11:05 EDT 2019. Contains 328294 sequences. (Running on oeis4.)