most recent 30 from http://mathoverflow.net 2013-05-24T09:54:23Z http://mathoverflow.net/feeds/user/16830 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/90050/self-avoiding-walk-on-mathbbz Sidharth Iyer 2012-03-02T15:49:57Z 2012-03-04T08:32:04Z

<p>This one is an <a href="http://math.stackexchange.com/questions/111377/self-avoiding-walk-on-mathbbz1.-" rel="nofollow">unanswered question</a> in Math.SE. I've posted it here because I think it deserves more attention.</p> <blockquote> <p>How many sequences $\{a_n\}$ exist satisfying: <p><em>a)</em> $a_1=0$ <p><em>b)</em> $\forall k\ge1 $ either $a_{k+1}=a_k+k$ or $a_{k+1}=a_k-k$ <p><em>c)</em> $a_i \neq a_j$ whenever $i \neq j$ <p><em>d)</em> $\mathbb{Z}=\{a_i\}_{i > 0}$</p> </blockquote> <p>Are the two below alternating sequences the only solutions?</p> <ul> <li>$a_{2k}=k$, $a_{2k+1}=-k$</li> <li>$a_{2k}=-k$, $a_{2k+1}=k$</li> </ul> <p>Also, it is known that <a href="http://mathworld.wolfram.com/RecamansSequence.html" rel="nofollow">Recamán's</a> <a href="https://oeis.org/A005132" rel="nofollow">sequence</a> satisfies <p><em>a)</em> $a_1=1$ and <em>b)</em>, <em>c)</em> as above </p>

http://mathoverflow.net/questions/90050/self-avoiding-walk-on-mathbbz Sidharth Iyer 2012-03-02T17:04:35Z 2012-03-02T17:04:35Z

@MartinBrandenburg Thank you for the help! I've changed the title.