Seq sugg'd: Moving (integer) average of primes: Do terms exist for any n?

[franktaw at netscape.net]

What you do in a case like this is define ", 0 if none exists".  Then 
you include a comment asking if there are any 0's.

This sequence is, IMO, definitely worth submitting.

Franklin T. Adams-Watters

-----Original Message-----
From: zak seidov <zakseidov at yahoo.com>

Dear SF gurus,
do terms exist for any n?
what about fini/full tags in such a case?
thanks, zak

%I A000001
%S A000001 
22,2,3,3,3,3,3,5,3,5,3,3,3,5,2,3,9,3,5,4,3,3,9,5,3,3,3,3,3,3,5,3,3,3,3,2,
3,11,2,3,3,33,3,3,6,2,5,3,3,9,3,3,3,2,2,3,5,3,5,3,5,3,3,3,4,3,3,4,3,3,3,5
,2,3,3,10,3,5,5,3,3,3,4,3,3,15,16,3,9,3,3,3,3,32,3,2,5,3,2,3,3,2,3,3,3,3,
2,3,3,2,3,3,3,5,4,3,5,2,6,5,4,3,3,3,3,3,3,15,2,8,7,3,15,3,7,4,6,3,13,3,5,
3,5,3,5,3,3,3,3,3,3,5,3,3,5,3,8,10,4,2,4,3,5,2,3,3,2,5,5,3,3,3,3,3,3,3,3,
3,2,3,3,3,5,2,3,6,2,3,3,7,3,4,3,2,6,3,5,5,2,3
%N A000001 a(n) = least k > 1 such that average (p(n)+...+p(n+k))/(k+1) 
is an
integer, p(n)=nth prime.
...