[seqfan] Re: tan(n). Was: Into subtleties of musical information

[Antti Karttunen]

On Tue, May 26, 2015 at 6:02 PM, Veikko Pohjola <veikko at nordem.fi> wrote:
> I do not see what relevance has the property tan(n) > n here. Let us take n=118554299812338354516058. Floor(tan(n)=1.

The relevance is quite direct as I was searching for cases of any n >
1 where floor(tan(n)) is somewhat near to n, and also wondering
whether it can ever be larger than n, as to estimate the possibility
of any other positive fixed points than 1 for floor(tan(n)).


Theoretically there might be also fixed points less than zero. And
even more theoretically, there might even exist a sequence of
iterations starting from some n which would never seem to set to a
fixed point, although I guess it would be even unlikelier than the
existence of these hypothetical fixed points < 0 or > 1.

But, like I said in PinkBox-comment 09:46 of https://oeis.org/draft/A258024

I would prefer more inclusive definition(s) for this/these sequence(s)
(this and A258022), because then it/they would offer a home for any
hypothetical orphan rarity (a fixed point < 0 or > 1), if such are
ever found, but not enough (3 terms) is found to create a wholly new
sequence.

(i.e. for numbers which when iterated with x -> floor(tan(x)) would
set to such a rare fixed point r, with at least r being one of them).

Please remember that the existence of all these extra fixed points is
just a remote possibility, and if your conjecture about their
nonexistence holds, then it will not affect the contents of any of
these sequences, but would just safeguard their elegance in case such
a monster is ever found.


Ystävällisin terveisin,

Antti


> Veikko
>
> Antti Karttunen kirjoitti 26.5.2015 kello 14.21:
>
>> 260515
>