A324673 Starting at n, a(n) is the length of the smallest interval containing all points 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, 1, 6, 3, 68, 72, 6, 13205, 31, 36, 10, 104, 836, 836, 43, 15, 570, 9518374, 57, 60, 1548481, 21, 203, 80, 87, 15466141, 71, 71, 28, 2436, 118129102, 6815959, 6815959, 6815959, 6815959, 86, 36, 560, 2261901, 2261901, 1091, 103, 103, 103, 6831, 45, 758, 499

Offset: 0

Author

David Nacin, Mar 10 2019

Keywords

• nonn

Examples

			For n=2, the points visited are 2,1,-1,-4,0.  The smallest interval containing these is [-4,2] which has length 6, thus a(2) = 6.
		

Crossrefs

Cf. A228474, A324660-A324692. Equals A248953 - A248952.

Programs

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 max(d['spots'])-min(d['spots'])