[seqfan] Re: Do 20 and 105 eventually reach a prime in these sequences?

[franktaw at netscape.net]

I think (though I don't have a proof) that the numbers grow 
exponentially. If that's the case, it doesn't really matter how small 
the base of the exponent is (as long as it's greater than 1); this only 
affects how soon one would expect to reach the point where most numbers 
do not reach a prime.

Franklin T. Adams-Watters

-----Original Message-----
From: Charles Greathouse <charles.greathouse at case.edu>

> Most *small* integers quickly reach a prime.  I'm confident that most
> integers do not.

Interesting.  The numbers don't grow that quickly, so I'd think you'd
typically reach a prime just 'by chance'.  I guess it all depends on
their rate of increase: the harmonic series diverges but the sum of
1/log(n log n) converges.

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