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A324672 Starting at n, a(n) is the sign of the farthest point from zero 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. In case of a tie, a(n)=0. 1
0, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0

COMMENTS

The only known value for which there is a tie (up to n=1000) happens at n=89.

LINKS

Table of n, a(n) for n=0..73.

EXAMPLE

For n=2, the points visited are 2,1,-1,-4,0. The farthest point from zero is -4, and sgn(-4) = -1, thus 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 sgn(x):

    if x:

        return x//abs(x)

    return 0

#Actual sequence

def a(n):

    d = trip(n)

    mx=max(d['spots'])

    mn=min(d['spots'])

    return sgn(mx+mn)

CROSSREFS

Cf. A228474, A324660-A324692.

Sequence in context: A070747 A070750 A011598 * A011599 A011600 A011601

Adjacent sequences:  A324669 A324670 A324671 * A324673 A324674 A324675

KEYWORD

sign

AUTHOR

David Nacin, Mar 10 2019

STATUS

approved

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Last modified October 17 22:44 EDT 2019. Contains 328134 sequences. (Running on oeis4.)