FORMULA
Limit_{N->oo} (Sum_{n=1..N} a(n)) / (Sum_{n=1..N} prime(n)) = 1. -_ _Alain Rocchelli_, Sep 30 2023
EXAMPLE
There are 2 primes less than 2^2, there are 2 primes between 2^2 and 3^2, 5 primes between 3^2 and 5^2, etc. [corrected by Jonathan Sperry, Aug 30 2013]
EXTENSIONS
Example corrected by Jonathan Sperry, Aug 30 2013
FORMULA
Limit_{N->oo} (Sum_{n=1..N} a(n)) / (Sum_{n=1..N} prime(n)) = 1. -Alain Rocchelli, Sep 30 2023
Discussion
Sat Sep 30
11:22
Alain Rocchelli: The proof of this formula seems to follow from the Prime Number Theorem.
Discussion
Fri Nov 11
11:34
Jon E. Schoenfield: (Please see the last paragraph of the OEIS Style Sheet.)
Mon Nov 14
17:08
Jianing Song: In any way, you have discarded all the former images, right? Especially the one labelled a050216_7.png and titled "Local Minima of Sequence A050216: Beam 2" (because you have uploaded it also to the former A357909)?
Wed Nov 16
11:33
Nicolas Vaillant: The graph of the ratio r(n) = 2 * a(n) / (n * (prime(n+1) - prime(n))) sums up on its own all the graphs of all the beams, that is why these graphs aren't usefull anymore.
LINKS
Nicolas Vaillant, <a href="/A050216/a050216_9.png">Graph of A050216(n) / (n * A001223(n))</a>
Nicolas Vaillant, <a href="/A050216/a050216_3.pdf">an elementary proof of Brocard's conjecture</a>
Discussion
Fri Nov 11
09:16
Joerg Arndt: This is a shining example of how to *not* proceed, a monumental waste of editors' time, messing up the edit history in the process. The OEIS will *not* publish your claimed proof of Brocard's conjecture.
LINKS
Nicolas Vaillant, <a href="/A050216/a050216_3.pdf">an elementary proof of Brocard's conjecture</a>
Nicolas Vaillant, <a href="/A050216/a050216_3.pdf">an elementary proof of Brocard's conjecture</a>
Discussion
Fri Nov 11
09:00
Nicolas Vaillant: The correct proof was uploaded. According to M.F.Hasler remark, it is better to remove this draft and do another one.
