A335045 Minimal common prime of two Goldbach partitions of 2n and 2(n+1) or zero if no common prime exists.

0, 3, 3, 5, 7, 3, 5, 7, 3, 5, 7, 23, 11, 13, 3, 5, 7, 0, 11, 13, 3, 5, 7, 47, 11, 13, 53, 17, 19, 3, 5, 7, 0, 11, 13, 3, 5, 7, 0, 11, 13, 83, 17, 19, 89, 23, 37, 0, 29, 31, 3, 5, 7, 3, 5, 7, 113, 11, 13, 0, 17, 19, 0, 23, 31, 131, 29, 31, 3, 5, 7, 0, 11, 13, 3, 5, 7, 0, 11, 13, 0, 17, 19, 167, 23, 37, 173

Offset: 2

Author

Ivan N. Ianakiev, May 21 2020

Keywords

• nonn

Comments

a(n) is the least prime p such that 2n-p is in A001359, or 0 if no such p exists. - Robert Israel, May 21 2020

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 = 3+13, so a(14/2) = a(7) = 3.
		

Links

• Index entries for sequences related to Goldbach conjecture

Crossrefs

Cf. A001359, A002372, A002373, A002375, A045917, A335046.

Programs

Maple

N:= 100:
P:= select(isprime, {seq(i,i=3..2*N-1,2)}):
T:= P intersect map(`-`,P,2):
f:= n -> subs(infinity=0, min(P intersect map(t -> 2*n-t, T))):
map(f, [$2..N]); # Robert Israel, May 21 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,Min[e[n]]];f/@Range[2,100]