A324662 Starting at n, a(n) is the difference of the number of left moves and the number of right moves 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, 2, 2, 4, 4, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 8, 6, 7, 7, 7, 9, 7, 7, 7, 7, 3, 7, 7, 7, 7, 8, 8, 8, 7, 7, 8, 9, 9, 9, 10, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12

Offset

0,3

Links

Table of n, a(n) for n=0..75.

David Nacin, a(n)/sqrt{n}

Example

For n=2, the points visited are 2,1,-1,-4,0 with the moves from 2 to 1, 1 to -1, and -1 to -4 being to the left, and the move from -4 to 0 being to the right, hence a(2) = 3 - 1 = 2.

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):
    return x//abs(x)
#Actual sequence
def a(n):
    d = trip(n)
    return sum(sgn(d['spots'][i] - d['spots'][i+1]) for i in range(d['turns']))

Crossrefs

Cf. A228474, A324660-A324692. Equals (A324661-A324660).

Sequence in context: A182923 A263856 A090277 * A024222 A196063 A205450

Adjacent sequences: A324659 A324660 A324661 * A324663 A324664 A324665

Keyword

nonn

Author

David Nacin, Mar 10 2019

Status

approved