A335045 - OEIS

%I #12 Jul 14 2020 23:47:23

%S 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,

%T 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,

%U 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

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

%C 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

%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>

%e 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.

%e 14 = 3+11 and 16 = 3+13, so a(14/2) = a(7) = 3.

%p N:= 100:

%p P:= select(isprime, {seq(i,i=3..2*N-1,2)}):

%p T:= P intersect map(`-`,P,2):

%p f:= n -> subs(infinity=0, min(P intersect map(t -> 2*n-t, T))):

%p map(f, [$2..N]); # _Robert Israel_, May 21 2020

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

%t e[n_]:=Intersection[d[n],d[n+1]]; f[n_]:=If[e[n]=={},0,Min[e[n]]];f/@Range[2,100]

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

%K nonn

%O 2,2

%A _Ivan N. Ianakiev_, May 21 2020