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A324683 Starting at n, a(n) is the number of times we move from a negative position 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. 1
0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 6, 6, 0, 0, 0, 33300, 0, 0, 4302, 0, 0, 0, 0, 58682, 0, 0, 0, 6, 154594, 18830, 18829, 18829, 18829, 0, 0, 2, 10283, 10282, 3, 1, 0, 0, 29, 0, 5, 3, 3, 3, 3, 5, 2, 0, 0, 0, 9, 9, 9, 21706, 21705, 21705, 21705, 21705, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Table of n, a(n) for n=0..65.

EXAMPLE

For n=41, the points visited are 41, 40, 38, 35, 31, 26, 20, 13, 5, -4, 6, -5, 7, -6, 8, -7, 9, -8, 10, -9, 11, -10, 12, -11, -35, -60, -34, -61, -33, -62, -32, -1, -33, 0.  The only time we revisit a spot is when we move from -1 to -33.  As this only occurs for one negative number, a(41)=1.

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}

#Actual sequence

def a(n):

    d = trip(n)

    return sum(1 for i in d['stuck'] if i < 0)

CROSSREFS

Cf. A228474, A324660-A324692.

Sequence in context: A281979 A172695 A172786 * A214373 A230299 A308235

Adjacent sequences:  A324680 A324681 A324682 * A324684 A324685 A324686

KEYWORD

nonn

AUTHOR

David Nacin, Mar 10 2019

STATUS

approved

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Last modified October 14 05:08 EDT 2019. Contains 327995 sequences. (Running on oeis4.)