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

[Neil Sloane]

Sean, here is why there is a chance that we will hit a prime eventually:

suppose the k-th term was about 10^2k. the chance of hitting a prime around
there is about 1/(2k) (ignoring constants). But the sum 1/(2k), k= m to
infinity, diverges,
although very very slowly (look at A004080)


On Mon, Oct 28, 2013 at 4:38 PM, Sean A. Irvine <sairvin at xtra.co.nz> wrote:

> 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.
>
>
>
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Neil J. A. Sloane, President, OEIS Foundation
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