|
%I #33 Jan 22 2024 06:19:13
%S 2,3,5,7,13,19,23,31,37,43,47,53,61,73,83,89,113,131,139,151,157,167,
%T 173,181,199,211,233,241,251,257,263,271,283,293,317,331,337,353,359,
%U 367,373,383,389,401,409,421,449,467,479,491,509,523
%N Primes followed by a larger-than-average prime gap.
%C Previous name was: Primes p(j) such that p(j+1)-p(j) > log(p(j)), where log is the natural logarithm.
%H Charles R Greathouse IV, <a href="/A082885/b082885.txt">Table of n, a(n) for n = 1..10000</a>
%F Conjecture: Limit_{N->oo} (Sum_{n=1..N} a(n)) / (Sum_{n=1..N} prime(n)) = e (A001113). - _Alain Rocchelli_, Dec 18 2023
%t Do[s=(Prime[n+1]-Prime[n])/Log[Prime[n]]//N; If[s>1, Print[{n, Prime[n], s}]], {n, 1, 1000}]
%t Transpose[Select[Partition[Prime[Range[100]],2,1],#[[2]]-#[[1]]> Log[#[[1]]]&]][[1]] (* _Harvey P. Dale_, Mar 15 2015 *)
%o (PARI) p=2;forprime(q=3,1e4,if(q-p>log(p),print1(p", "));p=q) \\ _Charles R Greathouse IV_, Feb 07 2012
%Y Cf. A082862, A082884, A002386.
%K nonn,nice
%O 1,1
%A _Labos Elemer_, Apr 17 2003
%E New name from _Charles R Greathouse IV_, Feb 07 2012
|
