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Jun 15, 2020 at 7:27 history edited CommunityBot
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Nov 16, 2016 at 13:37 vote accept T. Amdeberhan
Nov 16, 2016 at 5:21 answer added Alexey Ustinov timeline score: 10
Nov 16, 2016 at 5:21 answer added Pietro Majer timeline score: 7
Nov 16, 2016 at 5:06 comment added T. Amdeberhan @AlexeyUstinov: Good. It makes it more curious to link these sequences to $y_n$.
Nov 16, 2016 at 5:04 comment added Alexey Ustinov The sequence $\{x_n\}$ (with arbitrary $k$) was mentioned in the "Strange and Surprising Saga of the Somos Sequences" by D. Gale (see his book "Tracking the automatic ant and other mathematical explorations"). Accordind to this article it was discovered by Dana Scott.
Nov 16, 2016 at 5:01 comment added T. Amdeberhan Thanks, again. I see no proof though. In any case, let us ask for $k>3$.
Nov 16, 2016 at 4:49 comment added Gerry Myerson Question 2 is also mentioned (for the case $k=3$) at the page in my link, the third comment, Benoit Cloitre, 28 July 2002.
Nov 16, 2016 at 4:40 comment added T. Amdeberhan @GerryMyerson: I understand, not so surprised. My main interest is question #2.
Nov 16, 2016 at 4:37 history edited T. Amdeberhan CC BY-SA 3.0
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Nov 16, 2016 at 4:37 comment added Gerry Myerson $x_n$, for $k=3$, is tabulated at oeis.org/A064098 with much information and many links. Undoubtedly, some other parameter values are also represented at OEIS.
Nov 16, 2016 at 3:54 history edited T. Amdeberhan CC BY-SA 3.0
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Nov 16, 2016 at 3:44 history asked T. Amdeberhan CC BY-SA 3.0