The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A062047

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A062047

Sum of odd numbers between consecutive primes.
(history; published version)

#14 by Michael De Vlieger at Sat Jul 16 17:15:36 EDT 2022

STATUS

proposed

approved

#13 by Michel Marcus at Sat Jul 16 12:20:17 EDT 2022

STATUS

editing

proposed

#12 by Michel Marcus at Sat Jul 16 12:20:11 EDT 2022

LINKS

Harry J. Smith, <a href="/A062047/b062047.txt">Table of n, a(n) for n=1,...,1000</a>

FORMULA

a(n) = {pprime(n+1) +p prime(n)}*{pprime(n+1) - pprime(n)-2}/4.

a(n) = (prime(n)+e(n) )*( e(n)-1 ), where e(n) = A001223(n) / 2, for n > 1.

MATHEMATICA

Plus@@Range[ #[[1]]+2, #[[2]]-2, 2]&/@Partition[Prime[Range[100]], 2, 1] [From _(* _Harvey P. Dale_, Aug 13 2009] *)

CROSSREFS

a(n)= ( p(n)+e(n) )*( e(n)-1 ), e(n) := A001223(n) / 2, for n > 1, cf. A062046.

Cf. A001223, A062046.

EXTENSIONS

OFFSET changed from 0,4 to 1,4 by Harry J. Smith, Jul 30 2009

STATUS

approved

editing

#11 by N. J. A. Sloane at Fri Dec 15 17:35:06 EST 2017

EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org) and _Jason Earls (zevi_35711(AT)yahoo.com), _, Jun 07 2001

Discussion

Fri Dec 15

17:35

OEIS Server: https://oeis.org/edit/global/2722

#10 by Charles R Greathouse IV at Fri Aug 19 00:41:52 EDT 2016

PROG

(PARI) { for (n=1, 1000, q=prime(n + 1); p=prime(n); a=(q + p)*(q - p - 2)/4; if (n==1, a=0); write("b062047.txt", n, " ", a) ) } [From _\\ _Harry J. Smith_, Jul 30 2009]

Discussion

Fri Aug 19

00:41

OEIS Server: https://oeis.org/edit/global/2553

#9 by N. J. A. Sloane at Thu Dec 05 19:54:53 EST 2013

AUTHOR

_Amarnath Murthy (amarnath_murthy(AT)yahoo.com), _, Jun 06 2001

Discussion

Thu Dec 05

19:54

OEIS Server: https://oeis.org/edit/global/2075

#8 by Russ Cox at Fri Mar 30 18:51:44 EDT 2012

MATHEMATICA

Plus@@Range[ #[[1]]+2, #[[2]]-2, 2]&/@Partition[Prime[Range[100]], 2, 1] [From _Harvey P. Dale (hpd1(AT)nyu.edu), _, Aug 13 2009]

Discussion

Fri Mar 30

18:51

OEIS Server: https://oeis.org/edit/global/252

#7 by Russ Cox at Fri Mar 30 17:24:19 EDT 2012

PROG

(PARI) { for (n=1, 1000, q=prime(n + 1); p=prime(n); a=(q + p)*(q - p - 2)/4; if (n==1, a=0); write("b062047.txt", n, " ", a) ) } [From _Harry J. Smith (hjsmithh(AT)sbcglobal.net), _, Jul 30 2009]

EXTENSIONS

OFFSET changed from 0,4 to 1,4 by _Harry J. Smith (hjsmithh(AT)sbcglobal.net), _, Jul 30 2009

Discussion

Fri Mar 30

17:24

OEIS Server: https://oeis.org/edit/global/133

#6 by N. J. A. Sloane at Thu Nov 11 07:34:06 EST 2010

LINKS

Harry J. Smith, <a href="/A062047/b062047.txt">Table of n, a(n) for n=1,...,1000</a>

KEYWORD

nonn,new

nonn

#5 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

OFFSET

0,1,4

LINKS

Harry J. Smith, <a href="b062047.txt">Table of n, a(n) for n=1,...,1000</a>

MATHEMATICA

Plus@@Range[ #[[1]]+2, #[[2]]-2, 2]&/@Partition[Prime[Range[100]], 2, 1] [From Harvey P. Dale (hpd1(AT)nyu.edu), Aug 13 2009]

PROG

(PARI) { for (n=1, 1000, q=prime(n + 1); p=prime(n); a=(q + p)*(q - p - 2)/4; if (n==1, a=0); write("b062047.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 30 2009]

KEYWORD

nonn,new

nonn

EXTENSIONS

OFFSET changed from 0,4 to 1,4 by Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 30 2009