# [seqfan] Re: Primes and prime remainders

Sun Oct 5 20:47:50 CEST 2014

```If a(n) is lesser of twin primes, then a(n+1)=a(n)+2;
otherwise, it is intuitively clear that a(n+1) is
the smallest prime of the form 2*a(n)+prime.
Indeed,it is known that between 2*k and 3*k, k>=2,
there is a prime (q )( El Bachraoui (2006)). But is there,
for prime k>=5, such a prime q such that q-2*k is a prime (r)?
In this case we have q=r+2*k, where q,k,r are primes.
It is similar to a special case of the  Lemoine's-Levy's
conjecture for odd prime (here q is prime)
[cf. A046927], but with additional condition r<k.
So, till now it is an unsolved problem.

Regards,

________________________________________
From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of Eric Angelini [Eric.Angelini at kntv.be]
Sent: 05 October 2014 12:03
To: Sequence Discussion list
Subject: [seqfan] Primes and prime remainders

Hello SeqFans,
Primes p(n) such that the remainder
of p(n)/p(n-1) is prime.
The seq P starts with p(1)=3 and is always
extended with the smallest possible
prime.

P=3,5,7,17,19,41,43,89,...

Example:
5/3--> remainder 2
7/5--> remainder 2
17/7--> remainder 3
19/17--> remainder 2
41/19--> remainder 3
43/41--> remainder 2
89/43--> remainder 3
etc.
Hope I didn't mistake somewhere.
Best.
É.

Catapulté de mon aPhone

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