A324663 - OEIS

%I #8 Mar 11 2019 20:43:21

%S 0,0,1,0,9,10,0,740,2,3,0,7,48,49,2,0,39,348242,3,4,59273,0,12,5,6,

%T 523146,3,4,0,177,3533234,241226,241225,241226,241227,3,0,28,101615,

%U 101614,93,5,4,5,420,0,49,34,35,23,24,84,13,4,5,0,262,261,260,221950

%N Starting at n, a(n) is the number of moves made away from zero 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.

%H David Nacin, <a href="/A324663/a324663.png">A324663(n)/A228474(n)</a>

%e 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, hence a(2) = 1.

%o (Python)

%o #Sequences A324660-A324692 generated by manipulating this trip function

%o #spots - positions in order with possible repetition

%o #flee - positions from which we move away from zero with possible repetition

%o #stuck - positions from which we move to a spot already visited with possible repetition

%o def trip(n):

%o     stucklist = list()

%o     spotsvisited = [n]

%o     leavingspots = list()

%o     turn = 0

%o     forbidden = {n}

%o     while n != 0:

%o         turn += 1

%o         sign = n // abs(n)

%o         st = sign * turn

%o         if n - st not in forbidden:

%o             n = n - st

%o         else:

%o             leavingspots.append(n)

%o             if n + st in forbidden:

%o                 stucklist.append(n)

%o             n = n + st

%o         spotsvisited.append(n)

%o         forbidden.add(n)

%o     return {'stuck':stucklist, 'spots':spotsvisited,

%o                 'turns':turn, 'flee':leavingspots}

%o #Actual sequence

%o def a(n):

%o     d = trip(n)

%o     return len(d['flee'])

%Y Cf. A228474, A324660-A324692

%K nonn

%O 0,5

%A _David Nacin_, Mar 10 2019