[seqfan] Re: A Xmas fractal tree

[Neil Sloane]

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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