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.

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, 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, 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

Offset

1,1

Comments

a(n) = A142972(n) + 1.

Links

Table of n, a(n) for n=1..91.

Example

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.

Prog

Contribution from Franklin T. Adams-Watters, Apr 09 2009: (Start)
(PARI) dividesany(n, m, d)=for(k=n, m, if(k%d==0, return(1))); 0
firstnondiv(n, m)=for(d=2, m+1, if(!dividesany(n, m, d), return(d)))
vector(100, k, firstnondiv(prime(k), prime(k+1))) (End)

Crossrefs

Cf. A142972.

Sequence in context: A351126 A127018 A083396 * A181110 A199959 A084892

Adjacent sequences: A142970 A142971 A142972 * A142974 A142975 A142976

Keyword

nonn

Author

Leroy Quet, Jul 14 2008

Extensions

More terms from Franklin T. Adams-Watters, Apr 09 2009

Status

approved