login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A335046 Maximal common prime of two Goldbach partitions of 2n and 2(n+1) or zero (if common prime does not exist). 1
0, 3, 5, 7, 7, 11, 13, 13, 17, 19, 19, 23, 23, 19, 29, 31, 31, 0, 37, 37, 41, 43, 43, 47, 47, 43, 53, 53, 43, 59, 61, 61, 0, 67, 67, 71, 73, 73, 0, 79, 79, 83, 83, 79, 89, 89, 79, 0, 97, 97, 101, 103, 103, 107, 109, 109, 113, 113, 109, 0, 113, 109, 0, 127, 127, 131, 131, 127, 137, 139, 139 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

Table of n, a(n) for n=2..72.

Index entries for sequences related to Goldbach conjecture

EXAMPLE

4 = 2+2 and 6 = 3+3. Since those are the only available Goldbach partitions and they have no common prime, a(4/2) = a(2) = 0. 14 = 3+11 and 16 = 5+11, so a(14/2) = a(7) = 11.

MAPLE

S:= proc(n) option remember; {seq((h-> `if`(

      andmap(isprime, h), h, [])[])([n+i, n-i]), i=0..n-2)}

    end:

a:= n-> max(0, (S(n) intersect S(n+1))[]):

seq(a(n), n=2..80);  # Alois P. Heinz, Jun 20 2020

MATHEMATICA

d[n_]:=Flatten[Cases[FrobeniusSolve[{1, 1}, 2*n], {__?PrimeQ}]]

e[n_]:=Intersection[d[n], d[n+1]]; f[n_]:=If[e[n]=={}, 0, Max[e[n]]];

f/@Range[2, 100]

CROSSREFS

Cf. A002372, A002373, A002375, A045917, A060308, A335045.

Sequence in context: A260940 A037464 A302564 * A060265 A172365 A297709

Adjacent sequences:  A335043 A335044 A335045 * A335047 A335048 A335049

KEYWORD

nonn

AUTHOR

Ivan N. Ianakiev, May 21 2020

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 5 12:24 EST 2021. Contains 349557 sequences. (Running on oeis4.)