A120937 Least prime such that the distance to the two adjacent primes is 2n or greater.

3, 5, 23, 53, 211, 211, 211, 1847, 2179, 2179, 3967, 16033, 16033, 24281, 24281, 24281, 38501, 38501, 38501, 38501, 38501, 58831, 203713, 206699, 206699, 413353, 413353, 413353, 1272749, 1272749, 1272749, 1272749, 2198981, 2198981, 2198981

Offset: 0

Author

T. D. Noe, Jul 21 2006

Keywords

• nonn

Comments

Erdos and Suranyi call these reclusive primes and prove that such a prime exists for all n. Except for a(0), the record values are in A023186.

Examples

			a(3)=53 because the adjacent primes 47 and 59 are at distance 6 and all smaller primes have a closer distance.
		

References

• Paul Erdős and Janos Suranyi, Topics in the theory of numbers, Springer, 2003.

Crossrefs

Cf. A023186, A087770, A330428.

Programs

Mathematica

k=2; Table[While[Prime[k]-Prime[k-1]<2n || Prime[k+1]-Prime[k]<2n, k++ ]; Prime[k], {n,0,40}]