A324666 Starting at n, a(n) is the total number of positive 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, 1, 2, 2, 7, 9, 3, 786, 6, 8, 4, 18, 50, 52, 8, 5, 71, 336258, 10, 12, 74949, 6, 21, 13, 15, 438113, 12, 14, 7, 245, 6219115, 299928, 299928, 299930, 299932, 14, 8, 59, 103544, 103544, 125, 16, 16, 18, 423, 9, 62, 48, 50, 37, 39, 106, 28, 18, 20, 10, 363

Offset

0,3

Links

Table of n, a(n) for n=0..56.

David Nacin, A324666(n)/A228474(n)

Example

For n=2, the points visited are 2,1,-1,-4,0.  As exactly two of these are positive, 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. Equals A228474 - A324665.

Sequence in context: A026563 A062305 A155063 * A011022 A070910 A189040

Adjacent sequences: A324663 A324664 A324665 * A324667 A324668 A324669

Keyword

nonn

Author

David Nacin, Mar 10 2019

Status

approved