A081531 Primes p such that (r-p)/log(p) > 2, where r is the next prime after p.

7, 113, 139, 199, 211, 293, 317, 523, 773, 839, 863, 887, 953, 1069, 1129, 1259, 1327, 1381, 1637, 1669, 1759, 1831, 1913, 1933, 1951, 2113, 2161, 2179, 2221, 2251, 2311, 2477, 2503, 2557, 2593, 2803, 2861, 2971, 3089, 3137, 3229, 3271, 3413, 3469, 3739

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

prime(j) such that (prime(j+1)-prime(j))/log(prime(j)) > 2.

Example

If p=1327 then r=1361 and (r-p)/log(p) = 34/log(1327) = 4.72834..., so 1327 is in the sequence.

Mathematica

Do[s=(Prime[n+1]-Prime[n])/Log[Prime[n]]//N; If[s>2, Print[Prime[n]]], {n, 1, 2000}]
Transpose[Select[Partition[Prime[Range[600]], 2, 1], (Last[#]-First[#])/ Log[ First[#]]>2&]][[1]] (* Harvey P. Dale, Jun 22 2014 *)

Crossrefs

Cf. A082862, A082884-A082886, A082889-A082891.

Sequence in context: A099153 A270121 A079296 * A142537 A084974 A156240

Adjacent sequences: A081528 A081529 A081530 * A081532 A081533 A081534

Keyword

nonn

Author

Labos Elemer, Apr 17 2003

Status

approved