A082889 Primes p such that (r-p)/log(p) > 4, where r is the next prime after p.

1327, 15683, 16141, 19333, 19609, 20809, 25471, 28229, 31397, 31907, 34061, 34981, 35617, 35677, 36389, 37907, 40289, 40639, 43331, 43801, 44293, 45893, 48679, 58831, 59281, 60539, 69263, 73189, 74959, 79699, 81463, 82073, 85933, 86629

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..2500 from Harvey P. Dale)

Crossrefs

Cf. A082862, A082884, A082885, A082886, A082888, A082890, A082891.

Programs

Mathematica

Do[s=(Prime[n+1]-Prime[n])/Log[Prime[n]]//N; If[s>4, Print[Prime[n]]], {n, 1, 2000}]
Transpose[Select[Partition[Prime[Range[10000]],2,1],(#[[2]]-#[[1]])/ Log[ #[[1]]]>4&]][[1]] (* Harvey P. Dale, Dec 10 2014 *)

Formula

prime(j) such that (prime(j+1)-prime(j))/log(prime(j)) > 4.