The On-Line Encyclopedia of Integer Sequences (OEIS)

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A143223

(Number of primes between n^2 and (n+1)^2) - (number of primes between n and 2n).
(history; published version)

#23 by Alois P. Heinz at Tue Sep 21 19:51:23 EDT 2021

STATUS

proposed

approved

#22 by Wesley Ivan Hurt at Tue Sep 21 13:19:35 EDT 2021

STATUS

editing

proposed

#21 by Wesley Ivan Hurt at Tue Sep 21 13:19:28 EDT 2021

COMMENTS

Contribution from _From _Jonathan Sondow_, Aug 07 2008: (Start)

FORMULA

a(n) = A014085(n) - A060715(n) (for n > 0) = [pi((n+1)^2) - pi(n^2)] - [pi(2n) - pi(n)] (for n > 1).

STATUS

proposed

editing

#20 by Michel Marcus at Tue Sep 21 13:10:32 EDT 2021

STATUS

editing

proposed

#19 by Michel Marcus at Tue Sep 21 13:10:25 EDT 2021

LINKS

T. Hashimoto, <a href="http://arxiv.org/abs/0807.3690"> On a certain relation between Legendre's conjecture and Bertrand's postulate</a>, arXiv:0807.3690 [math.GM], 2008.

M. Hassani, <a href="http://arXiv.org/abs/math/0607096"> Counting primes in the interval (n^2,(n+1)^2)</a>, arXiv:math/0607096 [math.NT], 2006.

J. Pintz, <a href="http://www.renyi.hu/~pintz/"> Landau's problems on primes</a>

STATUS

approved

editing

#18 by Charles R Greathouse IV at Fri May 30 14:23:21 EDT 2014

STATUS

editing

approved

#17 by Charles R Greathouse IV at Fri May 30 14:23:10 EDT 2014

LINKS

Vincenzo Librandi, <a href="/A143223/b143223.txt">Table of n, a(n) for n = 0..10000</a>

PROG

(PARI) a(n)=sum(k=n^2+1, n^2+2*n, isprime(k))-sum(k=n+1, 2*n, isprime(k)) \\ Charles R Greathouse IV, May 30 2014

STATUS

approved

editing

#16 by Charles R Greathouse IV at Fri May 30 14:21:48 EDT 2014

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proposed

approved

#15 by Vincenzo Librandi at Fri May 30 14:12:46 EDT 2014

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editing

proposed

Discussion

Fri May 30

14:21

Charles R Greathouse IV: Thanks!

#14 by Vincenzo Librandi at Fri May 30 14:12:30 EDT 2014

LINKS

Vincenzo Librandi, <a href="/A143223/b143223.txt">Table of n, a(n) for n = 0..10000</a>

STATUS

proposed

editing