[seqfan] Re: Concatenate distances from n to prevprime and nextprime

Jack Brennen jfb at brennen.net
Mon Jan 11 18:14:30 CET 2010

Eric Angelini wrote:
> I've looked for a 3rd loop -- but couldn't find any, in the
> range n=1 to 1000. Is there a possible 3rd loop somewhere?

I'd conjecture there is no 3rd loop.  In fact, I'd conjecture
that there are only 73 numbers >= 3 which do not iterate to a
smaller number, and that the largest of these is 2503, which
iterates to 2618.  Any loop must necessarily contain a number
which does not iterate to a smaller number, and all of the 73
numbers end up in one of the two loops you already described.

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