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 A324671 Starting at n, a(n) is the distance from zero of the farthest point 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. 1
 0, 1, 4, 3, 47, 46, 6, 6843, 23, 22, 10, 72, 471, 470, 29, 15, 352, 4843985, 39, 38, 891114, 21, 102, 57, 56, 7856204, 45, 44, 28, 1700, 61960674, 3702823, 3702824, 3702825, 3702826, 51, 36, 370, 1213998, 1213997, 596, 62, 61, 60, 3855, 45, 417, 260, 261, 237 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS David Nacin, A324671 David Nacin, A324671(n)/A228474(n) EXAMPLE For n=2, the points visited are 2,1,-1,-4,0.  Of those the one farthest from zero is -4 with a distance of 4, hence a(2) = 4. 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 max(abs(i) for i in d['spots']) CROSSREFS Cf. A228474, A324660-A324692.  Equals max(A248953, -A248952). Sequence in context: A025175 A248247 A016504 * A249226 A328193 A273878 Adjacent sequences:  A324668 A324669 A324670 * A324672 A324673 A324674 KEYWORD nonn AUTHOR David Nacin, Mar 10 2019 STATUS approved

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Last modified August 5 18:53 EDT 2021. Contains 346488 sequences. (Running on oeis4.)