primal music

Jon Awbrey jawbrey at
Wed May 23 19:16:49 CEST 2007


the recent note on turning seqs into songs reminded me ...
one of the reasons that i called those dubly recursive
factorizations of integers "riffs" (qv) was because of
the notelike pictures they gave, reminiscent of things
like arpeggios and flam paradiddles and such.  i meant
to knock on some music theorist's door someday but did
not get around to it.  might be worth a pluck or three.


inquiry e-lab:
arisbe e-forum:
zhongwen wp:
wp review:

Good point,

3 = 1(1+2)
5 = 1(1+4)
7 = 1(1+6)

So all odd numbers should, trivially, be in the sequence. Thanks!

-----Original Message-----

On 5/23/07, Andrew Plewe <aplewe at> wrote:
> sequence one: integers which do not satisfy x^2 = y^2 + A(n):
> 1,2,3,4,5,6,7,9,10,13,14,17,18,19,22,23,25,26,29,30,31,34,38,etc...
> (i.e., integers which cannot be expressed as n(n+E), where E is an even
> integer greater than zero)

Why 3 belong to this sequence?

2^2 = 1^2 + 3
3 = n*(n+E)  for n=1, E=2.


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