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 A324682 Starting at n, a(n) is the sign of the of the closest nonzero point to zero visited for which the next move is a step 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. In the case of a tie, or if the set of points is empty, we set a(n)=0. 0
 0, 0, -1, 0, -1, 1, 0, -1, -1, 1, 0, -1, -1, 1, -1, 0, 1, 0, -1, 1, 1, 0, -1, -1, 1, 0, -1, 1, 0, -1, -1, -1, -1, 1, 1, -1, 0, -1, -1, -1, -1, -1, -1, 1, 1, 0, -1, -1, 1, -1, 1, 1, -1, -1, 1, 0, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 0, -1, 1, 0, -1, -1, -1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,18 LINKS EXAMPLE For n=9, the points visited are 9, 8, 6, 3, -1, 4, -2, 5, -3, -12, -22, -11, 1, 14, 0. The three times moves are made away from zero happen at -3, -12 and 1. The closest of these is to zero is 1 and thus a(9) = sgn(1) = 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 sgn(x):     if x:         return x//abs(x)     return 0 def maxorzero(x):     if x:         return max(x)     return 0 def minorzero(x):     if x:         return min(x)     return 0 #Actual sequence def a(n):     d = trip(n)     neg=maxorzero([i for i in d['flee'] if i < 0])     pos=minorzero([i for i in d['flee'] if i > 0])     if neg and not pos:         return -1     return -sgn(neg+pos) CROSSREFS Cf. A228474, A324660-A324692. Sequence in context: A286055 A140318 A060584 * A098725 A284939 A188260 Adjacent sequences:  A324679 A324680 A324681 * A324683 A324684 A324685 KEYWORD sign AUTHOR David Nacin, Mar 10 2019 STATUS approved

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Last modified September 20 10:10 EDT 2019. Contains 327229 sequences. (Running on oeis4.)