A122845 - OEIS

%I #11 Sep 22 2021 09:11:35

%S 3,3,3,3,3,3,0,5,5,5,3,3,3,7,3,3,3,3,5,3,3,0,5,5,5,7,5,5,3,3,3,7,3,3,

%T 7,3,3,3,3,5,3,3,5,3,3,0,5,5,5,7,5,5,7,5,5,3,3,3,7,3,3,7,3,3,7,3,0,5,

%U 5,5,11,5,5,17,5,5,23,5,0,0,7,7,7,11,7,7,11,7,7,11,7,3,3,3,0,3,3,13,3,3,13

%N Triangle read by rows, 3<=k<=n: T(n,k) = smallest prime p such that 2*k-p and 2*n-p are prime, T(n,k) = 0 if no such p exists.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>

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

%F T(A098090(n),3) = 2*A098090(n) - A085090(A098090(n)-1) = 3.

%t T[n_, k_] := Module[{p}, For[p = 2, p < 2n && p < 2k, p = NextPrime[p], If[PrimeQ[2n - p] && PrimeQ[2k - p], Return[p]]]; 0];

%t Table[T[n, k], {n, 3, 16}, {k, 3, n}] // Flatten (* _Jean-François Alcover_, Sep 22 2021 *)

%Y Cf. A098090.

%K nonn,tabl

%O 3,1

%A _Reinhard Zumkeller_, Sep 14 2006