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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
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, -1, -2, -1, 0, -6, -1, -1, -3, -2, -1, -1, 0, -4, -1, -1, -1, -1, -3, -2, -1, 0, -1, -2, -1, -3, -2, -1, -1, -2, -1, 0, -1, -1, -6, -1, -4, -3, -2, -1, -1, -1, 0, -3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..67.

EXAMPLE

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.

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['spots'] if i < 0])

CROSSREFS

Cf. A228474, A324660-A324692.

Sequence in context: A285914 A096875 A194514 * A258260 A094713 A123517

Adjacent sequences:  A324664 A324665 A324666 * A324668 A324669 A324670

KEYWORD

sign

AUTHOR

David Nacin, Mar 10 2019

STATUS

approved

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Last modified July 29 17:41 EDT 2021. Contains 346346 sequences. (Running on oeis4.)