Number of steps required to reach zero in the wrecker ball sequence starting with n: On the k-th step (k = 1, 2, 3, ...) move a distance of k in the direction of zero. If the result has occurred before, move a distance of k away from zero instead. Set a(n) = -1 if 0 is never reached.
(history;
published version)
LINKS
Gordon Hamilton, <a href="http://www.youtube.com/watch?v=mQdNaofLqVc&feature=youtu.be">Wrecker Ball Sequences</a>, Video, 2013. [The sequence is mentioned about 4.5 minutes in to the video. The video begins by discussing A005132. - N. J. A. Sloane, Apr 25 2019]
Discussion
Thu May 16
01:32
OEIS Server: https://oeis.org/edit/global/2815
LINKS
Gordon Hamilton, <a href="http://www.youtube.com/watch?v=mQdNaofLqVc&feature=youtu.be">Wrecker Ball Sequences</a>, Video, 2013. [The sequence is mentioned about 4.5 minutes in to the video. The video begins by discussing A005132. - _N. J. A. Sloane_, Apr 25 2019]
Discussion
Tue Apr 09
10:19
Peter Luschny: I agree.
COMMENTS
(Is it proved or only conjectured?)
LINKS
Hans Havermann, <a href="http://gladhoboexpress.blogspot.com/2019/04/sharp-peaks-and-high-plateaus.html">Sharp peaks and high plateaus</a> An overview of large knowns and unknowns up to index 10^6.
Discussion
Tue Apr 09
08:42
Hans Havermann: I've removed Daniel's comment. Altering an existing comment does seem to be an intrusive way to ask a question. That's why we have the Sequence Fanatics Discussion list.
Discussion
Mon Apr 08
22:31
Michael B. Porter: If m is the n-th triangular number m = 1+2+...+n, then doesn't the wrecker ball sequence go m, m-1, m-1-2, ..., m-1-2-...-k = 0? So there are n steps to reach 0.
LINKS
Hans Havermann, <a href="http://gladhoboexpress.blogspot.com/2019/04/sharp-peaks-and-high-plateaus.html">Sharp peaks and high plateaus</a> overview of large unknowns up to index 10^6
Discussion
Sun Apr 07
10:39
Hans Havermann: Daniel, if your "is it proved or only conjectured" refers to Neil's added escape clause, my take is that it will always be an open question, but only because we do not have the ability or time to resolve large finite results. Like a random one-dimensional walk, I see no reason why values should escape to infinity.
10:43
Hans Havermann: Oops, sorry Daniel. I see now where you placed your comment. So I take my answer back, if only I could.
COMMENTS
(Is it proved or only conjectured?)
Discussion
Mon Apr 01
21:11
Daniel Forgues: Since I can only add pink box comments after I save an edit, I had to first save my comment as an edit. It would be convenient to be able to do a pink box comment without the need to do an edit.
