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A122845 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.

%I A122845 #12 Feb 16 2025 08:33:02
%S A122845 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 A122845 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 A122845 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 A122845 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 A122845 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>
%H A122845 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%F A122845 T(A098090(n),3) = 2*A098090(n) - A085090(A098090(n)-1) = 3.
%t A122845 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 A122845 Table[T[n, k], {n, 3, 16}, {k, 3, n}] // Flatten (* _Jean-François Alcover_, Sep 22 2021 *)
%Y A122845 Cf. A098090.
%K A122845 nonn,tabl
%O A122845 3,1
%A A122845 _Reinhard Zumkeller_, Sep 14 2006