A324661 Starting at n, a(n) is the total number of moves made to the left 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, 3, 2, 14, 15, 3, 864, 8, 9, 4, 15, 64, 65, 10, 5, 62, 390904, 13, 14, 66452, 6, 29, 18, 19, 610401, 15, 16, 7, 218, 4434563, 266008, 266007, 266008, 266009, 17, 8, 51, 106681, 106680, 128, 21, 20, 21, 505, 9, 77, 60, 61, 46, 47, 110, 35, 22, 23, 10, 327

Offset

0,3

Links

Table of n, a(n) for n=0..56.

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 the only ones to the left, hence a(2)=3.

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}
#Actual sequence
def a(n):
    d = trip(n)
    return sum(1 for i in range(d['turns']) if d['spots'][i+1] < d['spots'][i])

Crossrefs

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

Sequence in context: A324012 A355259 A231183 * A163355 A214885 A145747

Adjacent sequences: A324658 A324659 A324660 * A324662 A324663 A324664

Keyword

nonn

Author

David Nacin, Mar 10 2019

Status

approved