[seqfan] Re: A conjecture for double primes

Hans Havermann gladhobo at teksavvy.com
Sat Apr 26 17:40:05 CEST 2014


A241536(78) = 6. A241536(79) = 6. It's likely that there are only three zeros: at indices 1, 2, and 5. I believe what Michel noted was that the number of *odd* terms was limited to indices 3, 4, 6, 8, and 11. This is a consequence (I think) of odd k being only ever the prime minus four and there is an increasing likelihood as we move along the sequence to infinity that another (even) k will be encountered before we reach it.


On Apr 26, 2014, at 6:59 AM, Vladimir Shevelev <shevelev at bgu.ac.il> wrote:

> Yesterday I have submitted a simple sequence A241536: "Smallest k>=1 such that numbers Prime(n) + or - k are both semiprimes, or a(n)=0 if there is no such k". The  behavior of the fist terms did not seem to bode special. Michel Marcus continued to calculate new terms, but starting with n=78 (prime(78)=397) and already up to n= 5*10^4 he obtained only zeros!! It is clear that large numbers have, as a rule,  more and more divisors, and one can expect that from a moment we will obtain sometimes zeros, but unexpectedly we obtained, maybe, ALL zeros.  If so, I think that it is a unique phenomenon of prime 397.




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