A082885 Primes followed by a larger-than-average prime gap.

2, 3, 5, 7, 13, 19, 23, 31, 37, 43, 47, 53, 61, 73, 83, 89, 113, 131, 139, 151, 157, 167, 173, 181, 199, 211, 233, 241, 251, 257, 263, 271, 283, 293, 317, 331, 337, 353, 359, 367, 373, 383, 389, 401, 409, 421, 449, 467, 479, 491, 509, 523

Offset: 1

Author

Labos Elemer, Apr 17 2003

Keywords

• nonn
• nice

Comments

Previous name was: Primes p(j) such that p(j+1)-p(j) > log(p(j)), where log is the natural logarithm.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A082862, A082884, A002386.

Programs

Mathematica

Do[s=(Prime[n+1]-Prime[n])/Log[Prime[n]]//N; If[s>1, Print[{n, Prime[n], s}]], {n, 1, 1000}]
Transpose[Select[Partition[Prime[Range[100]],2,1],#[[2]]-#[[1]]> Log[#[[1]]]&]][[1]] (* Harvey P. Dale, Mar 15 2015 *)

PARI

p=2;forprime(q=3,1e4,if(q-p>log(p),print1(p", "));p=q) \\ Charles R Greathouse IV, Feb 07 2012

Formula

Conjecture: Limit_{N->oo} (Sum_{n=1..N} a(n)) / (Sum_{n=1..N} prime(n)) = e (A001113). - Alain Rocchelli, Dec 18 2023

Extensions

New name from Charles R Greathouse IV, Feb 07 2012