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

0,1

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.

References

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

Links

Table of n, a(n) for n=0..34.

Example

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

Mathematica

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

Crossrefs

Cf. A023186, A087770, A330428.

Sequence in context: A036952 A065720 A148554 * A075307 A100302 A290384

Adjacent sequences: A120934 A120935 A120936 * A120938 A120939 A120940

Keyword

nonn

Author

T. D. Noe, Jul 21 2006

Status

approved