A324684 Starting at n, a(n) is the number of times we move from a positive spot 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, 31, 0, 0, 0, 1, 1, 1, 0, 0, 3, 25871, 0, 0, 6154, 0, 0, 0, 0, 30429, 0, 0, 0, 9, 422464, 25055, 25055, 25056, 25057, 0, 0, 0, 9685, 9685, 5, 0, 0, 1, 20, 0, 3, 1, 1, 0, 0, 5, 0, 0, 0, 0, 17, 17, 17, 15244, 15244, 15245, 15246, 15247, 1, 0

Offset

0,8

Links

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

Example

For n=43, the points visited are 43, 42, 40, 37, 33, 28, 22, 15, 7, -2, 8, -3, 9, -4, 10, -5, 11, -6, 12, -7, 13, -8, 14, -9, -33, -58, -32, -59, -31, -60, -30, 1, 33, 0.  The only time we revisit a spot is when we move from 1 to 33.  As this only occurs for one positive number, a(43)=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: A140762 A028363 A091511 * A213070 A221432 A085012

Adjacent sequences: A324681 A324682 A324683 * A324685 A324686 A324687

Keyword

nonn

Author

David Nacin, Mar 10 2019

Status

approved