# [seqfan] Re: A079039(8), decreasing trunc(cosh(n))

Hagen von Eitzen math at von-eitzen.de
Thu Jul 29 22:47:05 CEST 2010

```On 28.07.2010 14:17, Richard Mathar wrote:
> http://list.seqfan.eu/pipermail/seqfan/2010-July/005445.html responded
>
> zs>  Subject: [seqfan] Re: A079039(8), decreasing trunc(cosh(n))
> zs>
> zs>  1. Mmca code with 2000-digit accuracy gives:
> zs>
> zs>  (assuming that fractional part  of cos(0)=3D1
> zs>  as  in  A079039)
> zs>
> zs>  1, 3, 22, 29, 45, 75, 135, 259, 863, 1786, 2483, 2538
>
> Indeed, confirmed. The cosh() grow large exponentially, and one has to turn
> the number of digits higher with diligence for the followup terms to get
> meaningful post-dot digits.
>
> RJM
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>

A few (very few) more:

? fy=1;b=1;for(n=1,100, while( (fb=frac(cosh(b))) >= fy, b++;
default(realprecision,16);default(realprecision,floor(log(cosh(b))/log(10))+30);frac(cosh(b)));
fy=fb; print1(b,", "); b++)
1, 3, 22, 29, 45, 75, 135, 259, 863, 1786, 2483, 2538, 5731, 16095,
*** cosh: user interrupt after 4mn, 52,910 ms.

I think "near misses" can be excluded as replacing "fy=fb" in the code
above with "fy=1.001*fb" produces the same result so far.

And here are the correspondig fractional parts:
0.5430806348
0.0676619957
0.0657957809
0.0210371943
0.0173986167
0.0071713891
0.0058681139
0.0048040405
0.0007641272
0.0006658490
0.0006113271
0.0005632015
0.0001432333
0.0000518392

So one might expect a new record after about 20000 more steps (i.e at