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, -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

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