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

1,1

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

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A082862, A082884, A002386.

Sequence in context: A165666 A154579 A233134 * A118371 A330968 A153591

Adjacent sequences: A082882 A082883 A082884 * A082886 A082887 A082888

Keyword

nonn,nice

Author

Labos Elemer, Apr 17 2003

Extensions

New name from Charles R Greathouse IV, Feb 07 2012

Status

approved