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 A324672 Starting at n, a(n) is the sign of the farthest point from zero visited 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 case of a tie, a(n)=0. 1
 0, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0 COMMENTS The only known value for which there is a tie (up to n=1000) happens at n=89. LINKS EXAMPLE For n=2, the points visited are 2,1,-1,-4,0. The farthest point from zero is -4, and sgn(-4) = -1, thus 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 sgn(x):     if x:         return x//abs(x)     return 0 #Actual sequence def a(n):     d = trip(n)     mx=max(d['spots'])     mn=min(d['spots'])     return sgn(mx+mn) CROSSREFS Cf. A228474, A324660-A324692. Sequence in context: A070747 A070750 A011598 * A330035 A011599 A011600 Adjacent sequences:  A324669 A324670 A324671 * A324673 A324674 A324675 KEYWORD sign AUTHOR David Nacin, Mar 10 2019 STATUS approved

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Last modified July 27 21:21 EDT 2021. Contains 346316 sequences. (Running on oeis4.)