A324664 Starting at n, a(n) is the smallest distance from zero for which the next move is a step away from zero, or zero if no such move is ever made, 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, 0, 1, 0, 3, 1, 0, 5, 4, 1, 0, 7, 6, 1, 4, 0, 7, 8, 7, 1, 2, 0, 5, 4, 1, 2, 7, 1, 0, 13, 2, 1, 10, 1, 1, 7, 0, 5, 1, 3, 2, 1, 10, 1, 2, 0, 17, 16, 1, 14, 1, 2, 11, 10, 1, 0, 1, 1, 17, 1, 15, 1, 1, 1, 11, 10, 0, 4, 1, 2, 1, 1, 1, 15, 1, 13, 1, 1, 0, 2, 1, 1

Offset

0,5

Links

Table of n, a(n) for n=0..81.

David Nacin, A324664(n)/sqrt(n)

Example

For n=2, the points visited are 2,1,-1,-4,0 with all moves being towards zero from the current position except for the move from -1 to -4.  Thus the closest distance to zero from which a move is made away from zero is 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([abs(i) for i in d['flee']])

Crossrefs

Cf. A228474, A324660-A324692

Sequence in context: A348016 A353092 A362564 * A011084 A347924 A341103

Adjacent sequences: A324661 A324662 A324663 * A324665 A324666 A324667

Keyword

nonn

Author

David Nacin, Mar 10 2019

Status

approved