A335046 Maximal common prime of two Goldbach partitions of 2n and 2(n+1) or zero (if common prime does not exist).
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
Offset: 2
Keywords
Examples
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.
Programs
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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]