A324681 Starting at n, a(n) is the sign of the closest nonzero position to 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 the cases of a tie or n=0, we set a(n)=0.

0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, -1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, -1, 0, 1, 1, 0, -1, 0, 1, 0, -1, 1, 1, 0, -1, -1, -1, -1, 1, 0, 1, 0, 0, 0, -1, 1, 0, -1, -1, 0, 1, 0, -1, 1, 0, 1, 1, 1, 0, -1, -1, 1, 1, 1, 0, -1, -1, -1, -1, 0, -1, 1, 0, 1, 0

Offset

0

Links

Table of n, a(n) for n=0..79.

Example

For n=14, the points visited are 14, 13, 11, 8, 4, -1, 5, -2, 6, -3, 7, -4, -16, -29, -15, 0. The closest of these to zero is -1, which is negative, thus a(14) = sgn(-1) = -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
def maxorzero(x):
    if x:
        return max(x)
    return 0
def minorzero(x):
    if x:
        return min(x)
    return 0
#Actual sequence
def a(n):
    d = trip(n)
    neg=maxorzero([i for i in d['spots'] if i < 0])
    pos=minorzero([i for i in d['spots'] if i > 0])
    return (-sgn(neg+pos) + [2, 0][sgn(neg)])*sgn(n)

Crossrefs

Cf. A228474, A324660-A324692.

Sequence in context: A093879 A117872 A291291 * A368909 A285249 A269027

Adjacent sequences: A324678 A324679 A324680 * A324682 A324683 A324684

Keyword

sign

Author

David Nacin, Mar 10 2019

Status

approved