login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A161623 Greatest n for which the Andrica-like conjectural inequalities, Prime[n+1]-Prime[n]-(1/k)*Sqrt[Prime[n] < 0, appear to fail to hold, for k = 1,2,3,4,..., based on empirical evidence. 0

%I

%S 30,430,3644,4612

%N Greatest n for which the Andrica-like conjectural inequalities, Prime[n+1]-Prime[n]-(1/k)*Sqrt[Prime[n] < 0, appear to fail to hold, for k = 1,2,3,4,..., based on empirical evidence.

%C This is a family of increasingly restrictive Andrica-like conjectures that all imply Legendre's conjecture.

%e Example: For k = 1, one needs n > 30 for the inequality to obtain, and it is conjectured that it holds for all n > 30. In words, the first such inequality says that we expect to see a new prime p(n+1) between p(n) and p(n)+ Sqrt(p(n)).

%K nonn

%O 1,1

%A _Daniel Tisdale_, Jun 15 2009

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 24 12:20 EDT 2020. Contains 337318 sequences. (Running on oeis4.)