A324665 Starting at n, a(n) is the total number of negative positions 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, 2, 0, 17, 17, 0, 939, 6, 6, 0, 8, 73, 73, 7, 0, 48, 445544, 10, 10, 57947, 0, 30, 16, 16, 782680, 11, 11, 0, 184, 2650008, 232081, 232079, 232079, 232079, 12, 0, 35, 109811, 109809, 123, 17, 15, 15, 577, 0, 82, 62, 62, 45, 45, 104, 32, 16, 16, 0, 281, 279

Offset

0,3

Links

Table of n, a(n) for n=0..57.

David Nacin, A324665(n)/A228474(n)

Example

For n=2, the points visited are 2,1,-1,-4,0.  As exactly two of these are negative, we have a(2)=2.

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}
#Actual sequence
def a(n):
    d = trip(n)
    return sum(1 for i in d['spots'] if i < 0)

Crossrefs

Cf. A228474, A324660-A324692

Sequence in context: A178987 A242569 A152154 * A349036 A361591 A261516

Adjacent sequences: A324662 A324663 A324664 * A324666 A324667 A324668

Keyword

nonn

Author

David Nacin, Mar 10 2019

Status

approved