# A problem sending a sequence

Tautócrona tautocrona at terra.es
Tue Nov 8 02:30:01 CET 2005

```I'm trying to send the following sequence to the OEIS:

Email address (required): tautocrona at terra.es

New sequence

initial terms here:
3,5,11

Brief description or definition of sequence (required for a new sequence):
The prime numbers n such that the primorial of n is surrounded by a pair of twin primes.

What is the value of the "index" or "subscript" of the initial term?
1

Give formula, recurrence or generating function if known:
a(n) is the n-th prime having the property that p#-1 and p#+1 are also primes

Give an example:
a(2) = 5 because 5#-1 = 209 and 5#+1 = 211 are both prime at the same time, and 3 is the
only prime less than 5 having this property.

Jose Brox conjecture that this sequence is finite and that its last member is 11. It has
been verified up to n=10000 with the program below.

Program to generate the sequence: (PARI)
produ=1;forprime(n=1,20000,produ=n*produ;if(isprime(produ+1)&isprime(produ-1),print(n),0))

Select keywords:
nonn, hard, more

The problem seems to be that the sequence has less than 4 elements listed. But I couldn't
find another member of the sequence and I conjecture that, indeed, the sequence is finite
and consist only of 3,5,11... but I can't mark the keywords "fini" and "full" because I'm
not sure at all about it.

But I think the seq is interesting enough to get its place in the OEIS.

Can NJAS put it by hand? Maybe is there a trick to upload seqs with less than 4 terms if
they are not known?

Regards. Jose Brox
http://espanol.groups.yahoo.com/group/Telecomunicacion/
ambroxius at terra.es