The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A324683 Starting at n, a(n) is the number of times we move from a negative position to a spot we have already 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. 1
 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 6, 6, 0, 0, 0, 33300, 0, 0, 4302, 0, 0, 0, 0, 58682, 0, 0, 0, 6, 154594, 18830, 18829, 18829, 18829, 0, 0, 2, 10283, 10282, 3, 1, 0, 0, 29, 0, 5, 3, 3, 3, 3, 5, 2, 0, 0, 0, 9, 9, 9, 21706, 21705, 21705, 21705, 21705, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS EXAMPLE For n=41, the points visited are 41, 40, 38, 35, 31, 26, 20, 13, 5, -4, 6, -5, 7, -6, 8, -7, 9, -8, 10, -9, 11, -10, 12, -11, -35, -60, -34, -61, -33, -62, -32, -1, -33, 0.  The only time we revisit a spot is when we move from -1 to -33.  As this only occurs for one negative number, a(41)=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} #Actual sequence def a(n):     d = trip(n)     return sum(1 for i in d['stuck'] if i < 0) CROSSREFS Cf. A228474, A324660-A324692. Sequence in context: A281979 A172695 A172786 * A214373 A230299 A308235 Adjacent sequences:  A324680 A324681 A324682 * A324684 A324685 A324686 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 16 20:11 EDT 2022. Contains 353720 sequences. (Running on oeis4.)