The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A324664 Starting at n, a(n) is the smallest distance from zero for which the next move is a step away from zero, or zero if no such move is ever made, 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, 0, 1, 0, 3, 1, 0, 5, 4, 1, 0, 7, 6, 1, 4, 0, 7, 8, 7, 1, 2, 0, 5, 4, 1, 2, 7, 1, 0, 13, 2, 1, 10, 1, 1, 7, 0, 5, 1, 3, 2, 1, 10, 1, 2, 0, 17, 16, 1, 14, 1, 2, 11, 10, 1, 0, 1, 1, 17, 1, 15, 1, 1, 1, 11, 10, 0, 4, 1, 2, 1, 1, 1, 15, 1, 13, 1, 1, 0, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS David Nacin, A324664(n)/sqrt(n) EXAMPLE For n=2, the points visited are 2,1,-1,-4,0 with all moves being towards zero from the current position except for the move from -1 to -4.  Thus the closest distance to zero from which a move is made away from zero is 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 minorzero(x):     if x:         return min(x)     return 0 #Actual sequence def a(n):     d = trip(n)     return minorzero([abs(i) for i in d['flee']]) CROSSREFS Cf. A228474, A324660-A324692 Sequence in context: A245095 A154791 A121440 * A011084 A341103 A021326 Adjacent sequences:  A324661 A324662 A324663 * A324665 A324666 A324667 KEYWORD nonn AUTHOR David Nacin, Mar 10 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 24 15:39 EDT 2021. Contains 347643 sequences. (Running on oeis4.)