[seqfan] Re: Do 20 and 105 eventually reach a prime in these sequences?
franktaw at netscape.net
franktaw at netscape.net
Wed Sep 14 06:35:36 CEST 2011
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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