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A324686 Starting at n, a(n) is the number of times we move away from zero from a negative position 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, 1, 0, 8, 8, 0, 409, 2, 2, 0, 2, 31, 31, 2, 0, 15, 201444, 3, 3, 25388, 0, 10, 5, 5, 347717, 3, 3, 0, 75, 874341, 103653, 103652, 103652, 103652, 3, 0, 10, 52376, 52375, 48, 5, 4, 4, 251, 0, 32, 23, 23, 16, 16, 44, 10, 4, 4, 0, 113, 112, 111, 129093 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..59.

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.  Of these, we move away from zero at -7, -19, 13, 12, 31, 51, and 27. Two of these are negative and thus a(11)=2.

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 sgn(x):

    if x:

        return x//abs(x)

    return 0

#Actual sequence

def a(n):

    d = trip(n)

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

CROSSREFS

Cf. A228474, A324660-A324692.

Sequence in context: A019960 A069527 A154492 * A155840 A056194 A200304

Adjacent sequences:  A324683 A324684 A324685 * A324687 A324688 A324689

KEYWORD

nonn

AUTHOR

David Nacin, Mar 10 2019

STATUS

approved

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Last modified May 26 15:29 EDT 2019. Contains 323597 sequences. (Running on oeis4.)