%I
%S 4,6,4,6,5,6,4,6,10,4,10,6,4,6,9,10,7,10,6,5,8,6,9,11,6,4,6,5,6,16,6,
%T 10,4,15,4,10,11,6,11,9,7,12,5,6,4,18,14,6,5,6,8,7,12,10,8,9,4,9,6,4,
%U 14,22,6,5,6,21,10,12,5,6,8,16,11,10,6,10,16,6,10,12,8,12,5,8,6,9,14,6,4,6,15
%N a(n) = the smallest positive integer that does not divide any integer k, where the nth prime <= k <= the (n+1)th prime.
%C a(n) = A142972(n) + 1.
%e The 15th prime is 47 and the 16th prime is 53. So we will consider the integers 47,48,49,50,51,52,53. Now, 1 divides each of these 6 integers. 2 divides 48, 50 and 52. 3 divides 48 and 51. 4 divides 48 and 52. 5 divides 50. 6 divides 48. 7 divides 49. 8 divides 48. But 9 does not divide any integer that is between 47 and 53. So a(15)=9, since 9 is the smallest positive integer that does not divide any integer between 47 and 53.
%o Contribution from _Franklin T. AdamsWatters_, Apr 09 2009: (Start)
%o (PARI) dividesany(n,m,d)=for(k=n,m,if(k%d==0,return(1)));0
%o firstnondiv(n,m)=for(d=2,m+1,if(!dividesany(n,m,d),return(d)))
%o vector(100,k,firstnondiv(prime(k),prime(k+1))) (End)
%Y Cf. A142972.
%K nonn
%O 1,1
%A _Leroy Quet_, Jul 14 2008
%E More terms from _Franklin T. AdamsWatters_, Apr 09 2009
