%I A127567
%S A127567 2,6,10,19,25,29,36,42,43,41,63,65,45,69,86,98,90,77,94,132,118,112,132,
%T A127567 120,131,133,150,128,203,220,163,175,161,176,168,171,206,233,236,250,
%U A127567 201,230,293,270,297,283,256,253,272,318,266,277,296,308,349,353,312
%N A127567 Given k, the product of the first n primes and starting with the first 
               prime at least 3 greater than k, a(n) is the number of consecutive 
               primes where p-k is also prime.
%H A127567 <a href="http://h.xerol.org/f/1primecheck.txt">http://h.xerol.org/f/1primecheck.txt</
               a>Shows applicable sequences of primes for n=2..9
%e A127567 For n = 2, k = 2*3 = 6. The first prime at least 3 greater than 6 is 
               11.
%e A127567 11-6 = 5, 13-6 = 7, 17-6 = 11, 19-6 = 13, 23-6 = 17, 29-6 = 23, all of 
               which are primes. 31-6 = 25 is not prime, so a(2) = 6 because there 
               are 6 prime terms.
%p A127567 with(numtheory): a:=proc(n) local k,p,c,ct,j: k:=product(ithprime(i),
               i=1..n); p:=nextprime(k+2); c:=pi(p): ct:=0: for j from c while isprime(ithprime(j)-k)=true 
               do ct:=ct+1: od: ct; end: seq(a(n),n=1..9); - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Apr 13 2007
%Y A127567 Sequence in context: A084481 A006553 A054273 this_sequence A005993 A028247 
               A065054
%Y A127567 Adjacent sequences: A127564 A127565 A127566 this_sequence A127568 A127569 
               A127570
%K A127567 nonn
%O A127567 1,1
%A A127567 Ellis M. Eisen (xerol(AT)xerol.org), Apr 02 2007
%E A127567 Corrected by Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 13 2007
%E A127567 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 23 2007