This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A324680 #6 Mar 11 2019 20:45:44 %S A324680 0,0,0,0,0,0,0,3442,0,0,0,27,140,139,0,0,84,3072845,0,0,638385,0,0,0, %T A324680 0,4869724,0,0,0,464,43807680,2117461,2117462,2117463,2117464,0,0,24, %U A324680 696919,696918,179,1,0,1,1920,0,148,86,85,84,83,190,63,0,0,0,1107 %N A324680 Starting at n, a(n) is the largest distance from zero among all positions from which a spot must be revisited on the next move, or zero if no such positions exist, 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. %H A324680 David Nacin, <a href="/A324680/a324680.png">A324680</a> %H A324680 David Nacin, <a href="/A324680/a324680_1.png">A324680(n)/A228474(n)</a> %e A324680 For n=11, the points visited are 11, 10, 8, 5, 1, -4, 2, -5, 3, -6, 4, -7, -19, -32, -18, -3, 13, 30, 12, 31, 51, 72, 50, 27, 51, 26, 0. The only position from which we are forced to revisit a spot is 27, which forces a return to 51. Since this is the only time this happens it is also has the largest distance from zero, thus a(11)=27. %o A324680 (Python) %o A324680 #Sequences A324660-A324692 generated by manipulating this trip function %o A324680 #spots - positions in order with possible repetition %o A324680 #flee - positions from which we move away from zero with possible repetition %o A324680 #stuck - positions from which we move to a spot already visited with possible repetition %o A324680 def trip(n): %o A324680 stucklist = list() %o A324680 spotsvisited = [n] %o A324680 leavingspots = list() %o A324680 turn = 0 %o A324680 forbidden = {n} %o A324680 while n != 0: %o A324680 turn += 1 %o A324680 sign = n // abs(n) %o A324680 st = sign * turn %o A324680 if n - st not in forbidden: %o A324680 n = n - st %o A324680 else: %o A324680 leavingspots.append(n) %o A324680 if n + st in forbidden: %o A324680 stucklist.append(n) %o A324680 n = n + st %o A324680 spotsvisited.append(n) %o A324680 forbidden.add(n) %o A324680 return {'stuck':stucklist, 'spots':spotsvisited, %o A324680 'turns':turn, 'flee':leavingspots} %o A324680 def maxorzero(x): %o A324680 if x: %o A324680 return max(x) %o A324680 return 0 %o A324680 #Actual sequence %o A324680 def a(n): %o A324680 d=trip(n) %o A324680 return maxorzero([abs(i) for i in d['stuck']]) %Y A324680 Cf. A228474, A324660-A324692. %K A324680 nonn %O A324680 0,8 %A A324680 _David Nacin_, Mar 10 2019