# A problem sending a sequence

Gerald McGarvey Gerald.McGarvey at comcast.net
Tue Nov 8 02:55:26 CET 2005

```Two sequences related to this:

A005234
2,3,5,7,11,31,379,1019,1021,2657,3229,4547,4787,11549,13649,18523,23801,24029,42209,145823,366439,392113
Primorial primes: primes p such that 1 + product of primes up to p is prime.

A006794
3,5,11,13,41,89,317,337,991,1873,2053,2377,4093,4297,4583,6569,13033,15877
-1 + product of primes up to p is prime.

Regards,
Gerald McGarvey

At 08:30 PM 11/7/2005, Tautócrona wrote:
>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