A324668 Starting at n, a(n) is the minimum positive point visited, or zero if no positive points are 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, 1, 2, 1, 1, 3, 1, 2, 1, 4, 1, 1, 1, 4, 5, 1, 1, 3, 1, 1, 6, 1, 2, 1, 1, 5, 1, 7, 1, 1, 2, 3, 1, 1, 7, 8, 1, 1, 2, 3, 5, 6, 1, 1, 9, 1, 2, 1, 4, 1, 1, 7, 8, 1, 10, 1, 2, 3, 1, 2, 1, 1, 1, 9, 10, 11, 1, 1, 1, 4, 5, 6, 7, 1, 9, 1, 1, 12, 1, 2, 3, 4, 5, 6, 1

Offset

0,4

Links

Table of n, a(n) for n=0..85.

Example

For n=2, the points visited are 2,1,-1,-4,0.  As 1 is the smaller of the two positive values, a(2) = 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}
def minorzero(x):
    if x:
        return min(x)
    return 0
#Actual sequence
def a(n):
    d = trip(n)
    return minorzero([i for i in d['spots'] if i > 0])

Crossrefs

Cf. A228474, A324660-A324692.

Sequence in context: A127704 A307662 A050873 * A128221 A327856 A175488

Adjacent sequences: A324665 A324666 A324667 * A324669 A324670 A324671

Keyword

nonn

Author

David Nacin, Mar 10 2019

Status

approved