cp's OEIS Frontend

A144105 Primes at the upper end of the gaps mentioned in A144104.

%I A144105 #21 Mar 18 2018 04:01:40
%S A144105 3,5,11,17,29,37,53,59,127,149,211,223,307,331,541,1361,1693,1973,
%T A144105 2203,2503,2999,3299,4327,4861,5623,5779,5981,6521,6947,7283,8501,
%U A144105 9587,10007,10831,11777,12197,12889,15727,16183,19661,31469,34123,35671,35729
%N A144105 Primes at the upper end of the gaps mentioned in A144104.
%C A144105 Firoozbakht conjecture: (prime(n+1))^(1/(n+1)) < prime(n)^(1/n), or
%C A144105 prime(n+1) < prime(n)^(1+1/n), which can be rewritten as: (log(prime(n+1))/log(prime(n)))^n < (1+1/n)^n. This suggests a weaker conjecture: (log(prime(n+1))/log(prime(n)))^n < e. - _Daniel Forgues_, Apr 28 2014
%H A144105 T. D. Noe, <a href="/A144105/b144105.txt">Table of n, a(n) for n = 1..176</a>
%H A144105 A. Kourbatov, <a href="http://arxiv.org/abs/1503.01744">Verification of the Firoozbakht conjecture for primes up to four quintillion</a>, arXiv:1503.01744 [math.NT], 2015.
%H A144105 Nilotpal Kanti Sinha, <a href="http://arxiv.org/abs/1010.1399">On a new property of primes that leads to a generalization of Cramer's conjecture</a>, arXiv:1010.1399 [math.NT], 2010.
%H A144105 Wikipedia, <a href="http://en.wikipedia.org/wiki/Firoozbakht%E2%80%99s_conjecture">Firoozbakht's conjecture</a>
%e A144105 Examples for (log(prime(n+1))/log(prime(n)))^n < (1+1/n)^n < e:
%e A144105 (log(3)/log(2))^1 = 1.58... < (1+1/1)^1 = 2 < e;
%e A144105 (log(1361)/log(1327))^217 = 2.14... < (1+1/217)^217 = 2.712... < e;
%e A144105 (log(8501)/log(8467))^1059 = 1.59... < (1+1/1059)^1059 = 2.716... < e;
%e A144105 (log(35729)/log(35677))^3795 = 1.69... < (1+1/3795)^3795 = 2.717... < e.
%e A144105 - _Daniel Forgues_, Apr 28 2014
%K A144105 nonn
%O A144105 1,1
%A A144105 _T. D. Noe_, Sep 11 2008