The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A103274 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A103274

Number of ways of writing prime(n) in the form 2*prime(i)+prime(j).
(history; published version)

#18 by N. J. A. Sloane at Mon Sep 24 16:53:14 EDT 2018

EXTENSIONS

Edited by N. J. A. Sloane at the suggestion of _Andrew S. Plewe_, Jul 14 2007

Discussion

Mon Sep 24

16:53

OEIS Server: https://oeis.org/edit/global/2767

#17 by N. J. A. Sloane at Tue May 02 11:35:29 EDT 2017

STATUS

proposed

approved

#16 by Michael De Vlieger at Mon May 01 23:13:33 EDT 2017

STATUS

editing

proposed

#15 by Michael De Vlieger at Mon May 01 23:13:26 EDT 2017

LINKS

Michael De Vlieger, <a href="/A103274/b103274.txt">Table of n, a(n) for n = 1..1000</a>

MATHEMATICA

Table[Function[q, Length@ Select[#, Function[s, And[Length@ s == 2, Length@ First@ s == 1, MemberQ[Last@ , 2], Length@ Last@ s == 2]]] &@ Map[SortBy[Flatten[FactorInteger[#] /. {{p_, e_} /; e > 1 :> ConstantArray[p, e], {p_, 1} /; p > 1 :> p, {1, 1} -> 1}] & /@ #, Length] &, Select[IntegerPartitions[q, {2}], And[! MemberQ[#, 1], Total@ Boole@ PrimeQ@ # == 1] &]]]@ Prime@ n, {n, 89}] (* Michael De Vlieger, May 01 2017 *)

STATUS

approved

editing

#14 by N. J. A. Sloane at Tue Apr 19 01:07:35 EDT 2016

AUTHOR

_Yasutoshi Kohmoto (zbi74583(AT)boat.zero.ad.jp), _, Jan 27 2005

Discussion

Tue Apr 19

01:07

OEIS Server: https://oeis.org/edit/global/2496

#13 by Jon E. Schoenfield at Wed Sep 16 06:16:01 EDT 2015

STATUS

editing

approved

#12 by Jon E. Schoenfield at Wed Sep 16 06:15:59 EDT 2015

EXTENSIONS

Edited by N. J. A. Sloane at the suggestion of _Andrew Plewe, _, Jul 14 2007

STATUS

approved

editing

#11 by Charles R Greathouse IV at Wed Jul 22 12:25:58 EDT 2015

STATUS

editing

approved

#10 by Charles R Greathouse IV at Wed Jul 22 12:25:55 EDT 2015

COMMENTS

Marnell conjectures that a(n) > 0 for n > 3. I find no exceptions below 10^9. [From _- _Charles R Greathouse IV_, May 04 2010]

REFERENCES

Geoffrey R. Marnell, "Ten Prime Conjectures", Journal of Recreational Mathematics 33:3 (2004-2005), pp. 193-196. [From _Charles R Greathouse IV_, May 04 2010]

PROG

(PARI) a(n, q=prime(n))=my(s); forprime(p=2, q\2-1, if(isprime(q-2*p), s++)); s \\ Charles R Greathouse IV, Jul 22 2015

STATUS

approved

editing

#9 by Russ Cox at Fri Mar 30 17:38:05 EDT 2012

FORMULA

a(n) = A046926(prime(n)). - _David Wasserman (dwasserm(AT)earthlink.net), _, Oct 08 2005

EXTENSIONS

More terms from _David Wasserman (dwasserm(AT)earthlink.net), _, Oct 08 2005

Discussion

Fri Mar 30

17:38

OEIS Server: https://oeis.org/edit/global/184