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A324668 Starting at n, a(n) is the minimum positive point visited, or zero if no positive 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, 1, 1, 2, 1, 1, 3, 1, 2, 1, 4, 1, 1, 1, 4, 5, 1, 1, 3, 1, 1, 6, 1, 2, 1, 1, 5, 1, 7, 1, 1, 2, 3, 1, 1, 7, 8, 1, 1, 2, 3, 5, 6, 1, 1, 9, 1, 2, 1, 4, 1, 1, 7, 8, 1, 10, 1, 2, 3, 1, 2, 1, 1, 1, 9, 10, 11, 1, 1, 1, 4, 5, 6, 7, 1, 9, 1, 1, 12, 1, 2, 3, 4, 5, 6, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..85.

EXAMPLE

For n=2, the points visited are 2,1,-1,-4,0.  As 1 is the smaller of the two positive 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 minorzero(x):

    if x:

        return min(x)

    return 0

#Actual sequence

def a(n):

    d = trip(n)

    return minorzero([i for i in d['spots'] if i > 0])

CROSSREFS

Cf. A228474, A324660-A324692.

Sequence in context: A127704 A307662 A050873 * A128221 A327856 A175488

Adjacent sequences:  A324665 A324666 A324667 * A324669 A324670 A324671

KEYWORD

nonn

AUTHOR

David Nacin, Mar 10 2019

STATUS

approved

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Last modified September 26 20:36 EDT 2020. Contains 337374 sequences. (Running on oeis4.)