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A142973 a(n) = the smallest positive integer that does not divide any integer k, where the n-th prime <= k <= the (n+1)th prime. 1

%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 n-th 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. Adams-Watters_, 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. Adams-Watters_, Apr 09 2009

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Last modified August 25 09:48 EDT 2019. Contains 326324 sequences. (Running on oeis4.)