[seqfan] Re: Sequence contains only three elements 2, 4 and 6

[Giovanni Resta]

On 03/30/2014 01:25 PM, Tw Mike wrote:
> Dear Andrew,
>
> Thanks for your searching method,it's powerful.
> There's another seq [6]:
> numbers n that n/2 is prime, n and 2n between twin prime.
> a[0] is 6, a[1] maybe extreme large or doesnt exist.

Here a(1) is 6, not a(0), because in OEIS all the lists
of "numbers n such that ...." start from index = 1.

In any case, it is immediate to see that 6 is the only term,
because if n/2 is prime and different from 3, then it
is of the form 3k+1 or 3k+2. Then, n+1 and n-1 cannot be
both primes because 2(3k+1)+1 = 3(2k+1) and 2(3k+2)-1 = 3(2k+1),
so either n+1 or n-1 is divisible by 3.

Giovanni