[seqfan] Re: Permutations of the natural numbers - subcategories needed?

[Brad Klee]

After, http://list.seqfan.eu/pipermail/seqfan/2018-April/018579.html , per
Antti's request :

As a first point the Wiki for "Permutation of nonnegative integers" states
uncountable cardinality. Whether this encourages or discourages
classification, I don't know. A few years ago when the yellowstone
permutation was proven a permutation, another investigation of various
N-permutations in the OEIS seemed to show that almost all were isospectral
to N in the following sense:

Choose prime p and count multiples of p up to term a(n). If for each p, the
quantity "n / count(n,p)~p" as n tends to infinity, call the permutation
isospectral to the natural numbers.

The prime spectrum is a useful notion akin to the Fourier transform, and
also easy to plot as a function of n. Unfortunately this metric makes
"interesting" permutations look much less interesting. Conversely,
permuting say 3N with the set of primes is not that interesting, but
produces a sequence where the spectral line for 3 does not even converge.

Cheers,

Brad