A324685 Starting at n, a(n) is the difference of the number of times we revisit spots coming from positive spots and the number of times we revisit spots coming from negative spots 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, -21, 0, 0, 0, 1, -5, -5, 0, 0, 3, -7429, 0, 0, 1852, 0, 0, 0, 0, -28253, 0, 0, 0, 3, 267870, 6225, 6226, 6227, 6228, 0, 0, -2, -598, -597, 2, -1, 0, 1, -9, 0, -2, -2, -2, -3, -3, 0, -2, 0, 0, 0, 8, 8, 8, -6462, -6461, -6460, -6459, -6458

Offset

0,8

Links

Table of n, a(n) for n=0..63.

David Nacin, A324685

David Nacin, A324685(n)/A228474(n)

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 sgn(x):
    if x:
        return x//abs(x)
    return 0
#Actual sequence
def a(n):
    d = trip(n)
    return sum(sgn(i) for i in d['stuck'])

Crossrefs

Cf. A228474, A324660-A324692. Equals A324684-A324683.

Sequence in context: A364863 A209614 A167263 * A224114 A110454 A265156

Adjacent sequences: A324682 A324683 A324684 * A324686 A324687 A324688

Keyword

sign

Author

David Nacin, Mar 10 2019

Status

approved