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 A324665 Starting at n, a(n) is the total number of negative positions 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 from zero instead. 2
 0, 0, 2, 0, 17, 17, 0, 939, 6, 6, 0, 8, 73, 73, 7, 0, 48, 445544, 10, 10, 57947, 0, 30, 16, 16, 782680, 11, 11, 0, 184, 2650008, 232081, 232079, 232079, 232079, 12, 0, 35, 109811, 109809, 123, 17, 15, 15, 577, 0, 82, 62, 62, 45, 45, 104, 32, 16, 16, 0, 281, 279 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS David Nacin, A324665(n)/A228474(n) EXAMPLE For n=2, the points visited are 2,1,-1,-4,0.  As exactly two of these are negative, we have a(2)=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} #Actual sequence def a(n):     d = trip(n)     return sum(1 for i in d['spots'] if i < 0) CROSSREFS Cf. A228474, A324660-A324692 Sequence in context: A178987 A242569 A152154 * A261516 A009198 A209123 Adjacent sequences:  A324662 A324663 A324664 * A324666 A324667 A324668 KEYWORD nonn AUTHOR David Nacin, Mar 10 2019 STATUS approved

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Last modified September 19 03:31 EDT 2021. Contains 347550 sequences. (Running on oeis4.)