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