The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A162417 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A162417

Find max {primes such that p < n^2, n = 2,3,...}, then the gap g(n) between that prime and its successor. This sequence is the sequence of differences {2n - g(n)}.
(history; published version)

#13 by Charles R Greathouse IV at Thu Sep 08 08:45:46 EDT 2022

PROG

(MAGMAMagma) [2*n-(NthPrime(#PrimesUpTo(n^2)+1)-NthPrime(#PrimesUpTo(n^2))): n in [2..100]]; // Vincenzo Librandi, Aug 02 2015

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#12 by N. J. A. Sloane at Sun Aug 02 17:26:47 EDT 2015

STATUS

proposed

approved

#11 by Vincenzo Librandi at Sun Aug 02 00:59:02 EDT 2015

STATUS

editing

proposed

#10 by Vincenzo Librandi at Sun Aug 02 00:58:52 EDT 2015

PROG

(MAGMA) [2*n-(NthPrime(#PrimesUpTo(n^2)+1)-NthPrime(#PrimesUpTo(n^2))): n in [2..100]]; // Vincenzo Librandi, Aug 02 2015

STATUS

proposed

editing

#9 by Wesley Ivan Hurt at Sat Aug 01 23:27:03 EDT 2015

STATUS

editing

proposed

#8 by Wesley Ivan Hurt at Sat Aug 01 23:26:20 EDT 2015

MAPLE

with(numtheory): A162417:=n->2*n-(ithprime(pi(n^2)+1)-ithprime(pi(n^2))): seq(A162417(n), n=2..100); # Wesley Ivan Hurt, Aug 01 2015

CROSSREFS

Cf. A058043.

STATUS

proposed

editing

#7 by Jon E. Schoenfield at Sat Aug 01 21:35:23 EDT 2015

STATUS

editing

proposed

#6 by Jon E. Schoenfield at Sat Aug 01 21:35:21 EDT 2015

NAME

We find Find max {primes such that p < n^2, n = 2,3,...}, then the gap g(n) between that prime and its successor. This sequence is the sequence of differences {2n - g(n)}.

FORMULA

a(n) = 2*n - A058043(n). - R. J. Mathar, Jul 13 2009

MATHEMATICA

f[n_] := 2 n - Prime[PrimePi[n^2] + 1] + Prime[PrimePi[n^2]]; Table[ f@n, {n, 2, 69}] [From _(* _Robert G. Wilson v_, Aug 17 2009] *)

STATUS

approved

editing

#5 by N. J. A. Sloane at Wed May 01 21:10:56 EDT 2013

EXTENSIONS

Edited by _N. J. A. Sloane, _, Jul 05 2009

Discussion

Wed May 01

21:10

OEIS Server: https://oeis.org/edit/global/1900

#4 by Russ Cox at Sat Mar 31 10:31:25 EDT 2012

AUTHOR

_Daniel Tisdale (daniel6874(AT)gmail.com), _, Jul 02 2009

Discussion

Sat Mar 31

10:31

OEIS Server: https://oeis.org/edit/global/716