A324683 Starting at n, a(n) is the number of times we move from a negative position to a spot we have already 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.

0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 6, 6, 0, 0, 0, 33300, 0, 0, 4302, 0, 0, 0, 0, 58682, 0, 0, 0, 6, 154594, 18830, 18829, 18829, 18829, 0, 0, 2, 10283, 10282, 3, 1, 0, 0, 29, 0, 5, 3, 3, 3, 3, 5, 2, 0, 0, 0, 9, 9, 9, 21706, 21705, 21705, 21705, 21705, 1, 0

Offset

0,8

Links

Table of n, a(n) for n=0..65.

Example

For n=41, the points visited are 41, 40, 38, 35, 31, 26, 20, 13, 5, -4, 6, -5, 7, -6, 8, -7, 9, -8, 10, -9, 11, -10, 12, -11, -35, -60, -34, -61, -33, -62, -32, -1, -33, 0.  The only time we revisit a spot is when we move from -1 to -33.  As this only occurs for one negative number, a(41)=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}
#Actual sequence
def a(n):
    d = trip(n)
    return sum(1 for i in d['stuck'] if i < 0)

Crossrefs

Cf. A228474, A324660-A324692.

Sequence in context: A281979 A172695 A172786 * A214373 A230299 A308235

Adjacent sequences: A324680 A324681 A324682 * A324684 A324685 A324686

Keyword

nonn

Author

David Nacin, Mar 10 2019

Status

approved