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

Author

Labos Elemer, Apr 17 2003

Keywords

• nonn

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

Formula

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