question about A033188 (Conjectural) minimum difference of an increasing arithmetic progression of n primes.

[Graeme McRae]

David,
I verified that n*30030+14933623 is prime for 0 <= n < 13, but I didn't 
check all the numbers smaller than 14933623 to see if any of them work. 
However, it's not surprising that A033189 decreases in places where the 
value of A033188 changes.  But in regions where A033188 is constant, A033189 
increases as we both expect.
--Graeme

----- Original Message ----- 
From: "David Wilson" <davidwwilson at comcast.net>
To: <njas at research.att.com>
Cc: "Sequence Fans" <seqfan at ext.jussieu.fr>
Sent: Thursday, January 26, 2006 1:10 PM
Subject: Re: question about A033188 (Conjectural) minimum difference of an 
increasing arithmetic progression of n primes.


> If the smallest element of an arithmetic progression of n primes (that is, 
> A033189(n)) is > n#, then modular arguments show that the difference (that 
> is, A033188(n)) must be >= n#.  A variation of the k-tuples conjecture 
> then asserts that A033188(n) = n#.  The empirical data on A033189 seem to 
> indicate that A033189(n) >= n# for n >= 8.
>
> The proved values for A033189(n) will be those for which A033189(n) are 
> known.
>
> Can someone please verify A033189(13).  I would have expected A033189 to 
> be increasing, but it ain't necessarily so.
>