[seqfan] A056198 - "Organic numbers"?

Antti Karttunen antti.karttunen at gmail.com
Tue Mar 29 15:52:36 CEST 2011


Could somebody more experienced than me,
check whether the sequence

is the same as mentioned in the various papers given under:



The formula for Moshe Klein's "organic numbers" is given at slide #20
of the following Power Point slide set:
(there seems to be two Youtube-presentations also,
at: http://www.youtube.com/watch?v=h00oXmwUbyY )

Think of what you may about the advertised deeper quantum
philosophical connections
of these "numbers", but at least the underlying combinatorial structure
seems to be well-defined, and as such merits our attention.
(And at least there should be a link from A056198 to the site mentioned.)

In any case, somehow this reminds me of Jon Awbrey's Riffs and Rotes,
which is also based on recursive (de)composing according to
tree structures restricted on certain ways.

So I'm wondering, would these "organic numbers" tree/partition structures
somehow allow a natural ("natural" again! ;-) bijection to the
(positive) integers?

How many ways we can devise a recursive (de)composition scheme of tree-like
structures, for which we can also assign some meaningful "semantics"?
(Okay, this is a very vague question, but think e.g. combinatorial games trees.)

Also, I think there's a seed of truth what the writer says in the
beginning of http://www.omath.org.il/image/users/112431/ftp/my_files/VDND9.pdf
about the children, and trying to understand their yet unschooled way
of thinking.


Antti Karttunen

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