[seqfan] Re: More terms for A195265 and A230305 ?

[Sean A. Irvine]

On 10/27/13 19:56, Neil Sloane wrote:
> Dear Seqfans, A195265 was created in 2011, but presumably we have better
> factoring algorithms now and more computers and
> more people and a bigger cloud.
>
> The definition is simple - start with 20 and keep
> applying the map  x -> A080670(x) until you reach a prime;
> A195264(20) will be the prime that is reached (or -1 if
> no prime is ever reached).
>
> A230305(n) is the number of steps to reach a prime,
> starting with n (or -1 if no prime is ever reached).
> The question then is, what is A230305(20)?
>
> Could someone extend A195265 and see what happens? (it could also use a
> b-file). It /should/ reach a prime sooner or later!
>
> Neil
>

A195264(20) has at least 193 digits.  Like Hans say, it is currently
blocked with a 178-digit composite.

Actually, it is far from clear to me that it /should/ reach a prime.
I have seen the same thing claimed for the Home Prime sequences,
but I don't believe any proof of such exists.  Naively, it might be
that the numbers are growing fast enough that the probability of
hitting a prime is dropping quick enough that it never happens, or
at least could be unbounded far into the sequence.  It would
definitely take someone with more math than me to answer that.

Sean.