A082888 Primes p such that (r-p)/log(p) > 3, where r is the next prime after p.

1129, 1327, 1669, 2179, 2477, 2971, 3137, 3271, 4297, 4831, 5119, 5351, 5531, 5591, 5749, 5953, 6491, 6917, 7253, 7759, 7963, 8389, 8467, 8893, 8971, 9551, 9973, 10009, 10399, 10531, 10799, 10909, 11743, 12163, 12853, 13063, 13187, 13933

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

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A082862, A082884, A082885, A082886, A082889, A082890, A082891.

Programs

Mathematica

Do[s=(Prime[n+1]-Prime[n])/Log[Prime[n]]//N; If[s>3, Print[Prime[n]]], {n, 1, 2000}]
Transpose[Select[Partition[Prime[Range[2000]],2,1],(Last[#]-First[#])/ Log[ First[ #]]>3&]][[1]] (* Harvey P. Dale, Apr 20 2013 *)

Formula

prime(j) such that (prime(j+1)-prime(j))/log(prime(j)) > 3.