The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A275768 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A275768

a(n) is the number of ways to express n = (prime(i) + prime(j))/2 when (prime(i) - prime(j))/2 also is prime.
(history; published version)

#47 by Susanna Cuyler at Sun Apr 08 09:21:21 EDT 2018

STATUS

proposed

approved

#46 by Wesley Ivan Hurt at Tue Apr 03 21:49:48 EDT 2018

STATUS

editing

proposed

#45 by Wesley Ivan Hurt at Tue Apr 03 21:24:55 EDT 2018

COMMENTS

Number of Goldbach partitions (p,q) of 2n such that |q-p|/2 is prime. For example, a(8) = 2; 2*8 = 16 has 2 Goldbach partitions (3,13) and (5,11). Both |13-3|/2 = 5 and |11-5|/2 = 3 are prime, so a(8) = 2. - Wesley Ivan Hurt, Apr 03 2018

FORMULA

a(n) = Sum_{i=1..n} A010051(n-i) * A010051(2n-i) * A010051(i). - Wesley Ivan Hurt, Apr 03 2018

CROSSREFS

Cf. A000040, A010051.

STATUS

approved

editing

#44 by N. J. A. Sloane at Tue May 23 22:03:32 EDT 2017

STATUS

editing

approved

#43 by N. J. A. Sloane at Tue May 23 22:03:29 EDT 2017

MATHEMATICA

(*example Example of a program to find first 1000 terms of a(n)*)

countOfPrimes = 0;

countOfPrimes2 = 0;

countOfPrimes3 = 0;

PnToUse = z;

distanceToCheck = PnToUse;

For[i = 0, i < distanceToCheck, i++,

STATUS

reviewed

editing

#42 by Paolo P. Lava at Tue May 23 08:20:54 EDT 2017

STATUS

proposed

reviewed

#41 by Jamie Morken at Sat May 20 23:39:56 EDT 2017

STATUS

editing

proposed

#40 by Jamie Morken at Sat May 20 23:38:47 EDT 2017

MATHEMATICA

(*example program to find first 1000 terms of a(n)*)

For[z = 0, z < 1000, z++,

countOfPrimes = 0;

countOfPrimes2 = 0;

countOfPrimes3 = 0;

PnToUse = z;

distanceToCheck = PnToUse;

For[i = 0, i < distanceToCheck, i++,

If[PrimeQ[2*PnToUse - i],

countOfPrimes++ If[PrimeQ[(2*PnToUse - i) - PnToUse],

countOfPrimes2++ If[PrimeQ[i], countOfPrimes3++]], ]]

Print[countOfPrimes3]]

(* Jamie Morken, May 20 2017 *)

STATUS

approved

editing

Discussion

Sat May 20

23:39

Jamie Morken: added alternate Mathematica code example

#39 by OEIS Server at Wed May 03 21:56:58 EDT 2017

LINKS

Michael De Vlieger, <a href="/A275768/b275768_1.txt">Table of n, a(n) for n = 0..10000</a>

#38 by N. J. A. Sloane at Wed May 03 21:56:58 EDT 2017

STATUS

proposed

approved

Discussion

Wed May 03

21:56

OEIS Server: Installed new b-file as b275768.txt.  Old b-file is now b275768_1.txt.