[seqfan] Re: A Xmas fractal tree

[Reinhard Zumkeller]

see https://oeis.org/draft/A253146, some narrative might be nice.
Best regards
Reinhard


2014-12-27 21:54 GMT+01:00 Neil Sloane <njasloane at gmail.com>:

> Eric's Christmas Tree sequence is very nice.
> The one that begins:
>
> 1, 2,3, 4,1,5, 6,2,3,7, 8, 9,4,1,5,10, 11,6,2,3,7,12, 13,14, 15,8,16, ...
>
> If we call it a fractal tree, not mentioning Christmas,
> then it could go into the OEIS, I think.
>
> Trees are legitimate mathematical shapes to study,
> just like spirals.
>
> Could someone add it (and
> reply with the A-number, so I can look for it on the editing
> stack (which is getting very big))?
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Sat, Dec 27, 2014 at 6:08 AM, Eric Angelini <Eric.Angelini at kntv.be>
> wrote:
>
> > Hello SeqFans,
> > Here is a fractal Xmas tree. Many thanks to all contributors who took the
> > time to read my posts so far – and a happy 2015 to the wonderful OEIS’
> > staff!
> > Best,
> > É.
> >
> >
> >
> >                                   1,
> >                                  2,3,
> >                                 4,1,5,
> >                                6,2,3,7,
> >                                   8,
> >                               9,4,1,5,10,
> >                             11,6,2,3,7,12,
> >                                 13,14,
> >                                15,8,16,
> >                            17,9,4,1,5,10,18,
> >                          19,11,6,2,3,7,12,20,
> >                         21,13,8,4,1,5,9,14,22,
> >                              23,15,16,24,
> >                                  25,
> >                            26,17,10,18,27,
> >                       28,19,11,6,2,3,7,12,20,29,
> >                      30,21,13,8,4,1,5,9,14,22,31,
> >                           32,23,15,16,24,33,
> >                                 34,35,
> >                               36,25,37,
> >                         38,26,17,10,18,27,39,
> >                    40,28,19,11,6,2,3,7,12,20,29,41,
> >                   42,30,21,13,8,4,1,5,9,14,22,31,43,
> >                 44,32,23,15,10,6,2,3,7,11,16,24,33,45,
> >                46,34,25,17,12,8,4,1,5,9,13,18,26,35,47,
> >                        48,36,27,19,20,28,37,49,
> >              50,38,29,21,14,10,6,2,3,7,11,15,22,30,39,51,
> >             52,40,31,23,16,12,8,4,1,5,9,13,17,24,32,41,53,
> >                      54,42,33,25,18,26,34,43,55,
> >                              56,44,45,57,
> >                                  58,
> >                                  ...
> >
> > Shape:
> > The width of the tree, at every stage, is given by the tree itself,
> > starting from the top (the successive widths, starting from the top, are
> > 1,2,3,4,1,5,6,2,3,7,...)
> >
> > Fractality:
> > If you “peel” the tree, it will reappear – unchanged (to “peel” is to
> > erase the first and last integer of each layer).
> >
> >
> >
> > _______________________________________________
> >
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> >
>
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