[seqfan] Re: patterns continue for larger numbers? generalised question

[Neil Fernandez]

In message <hNolpKA96dmdFwrS at borve.org>, Neil Fernandez
<primeness at borve.org> writes
>In message <qtdnxXAr2dmdFwp2 at borve.org>, Neil Fernandez
><primeness at borve.org> writes
>
>>A generalised question that comes to mind is this:
>>
>>is there any (n,t,u) (t>1,u>1) for which the sequence
>>
>>a(1)=n;
>>a(i+1) = a(i)/t if n|t, otherwise a(i+1)= a(i) + smallest uth power > i
>>
>>does not reach a cycle?
>
>Typo. The second line of the definition should read:
>
>a(i+1) = a(i)/t if t|a(i),
>               otherwise a(i+1)= a(i) + smallest uth power > i

Argh - my apologies - another typo!

The definition of the sequence (n,t,u) (with t,u > 1) is this

a(1) = n
a(i+1) = a(i)/t if t|a(i),
   otherwise a(i+1)= a(i) + smallest uth power > a(i)

So Ali's sequences are (n,2,2), which we know always come back to 1 or
11 for n <= 1200000.

Is there an (n,t,u) that can be shown to explode?

Neil

-- 
Neil Fernandez