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A082885
Primes followed by a larger-than-average prime gap.
6
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
KEYWORD
nonn,nice
AUTHOR
Labos Elemer, Apr 17 2003
EXTENSIONS
New name from Charles R Greathouse IV, Feb 07 2012
STATUS
approved