[seqfan] Re: Sequences with nice graphs / "Entanglement permutations"

[Antti Karttunen]

On Sat, Jan 25, 2014 at 1:08 AM, Antti Karttunen
<antti.karttunen at gmail.com> wrote:

>
> So, for Katarzyna's A135141, those two pairs of complementary sets are
> primes/composites and even/odd numbers, and the latter occur as one of
> the pairs in all examples I have submitted so far. But of course one
> does not need to delimit oneself to that. E.g. what comes if one
> "entangles" pair primes/composites with pair composites/primes, in a
> similar way?
> Is it already in OEIS? (Should result a self-inverse permutation).

Yes, it is in OEIS already. Namely, Katarzyna's
http://oeis.org/A135044
"a(1)=1, then a(p_n)=c_a(n), a(c_n)=p_a(n), where p_n - n-th prime,
c_n - n-th composite."

Would it be possible for anybody to compute this up to a "some more"
terms, to see whether it look as nice as A135141 ?

Somebody with a capable computer, as these "entanglement permutations"
quickly amplify any asymmetry between the growth rates of the
complementary pair(s) they operate on. Cf. http://oeis.org/A007097
what to expect.

And there also a lot's of other permutations which might make nice
graphs if their terms were computed up to a few thousands.

Is there any simple way to search for sequences which have a user
submitted b-file vs. those which have it automatically computed from
the terms given on data-rows?


Yours,

Antti Karttunen