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.

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, 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, 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

Offset: 3

Author

Reinhard Zumkeller, Sep 14 2006

Keywords

• nonn
• tabl

Links

• Eric Weisstein's World of Mathematics, Goldbach Partition
• Index entries for sequences related to Goldbach conjecture

Crossrefs

Cf. A098090.

Programs

Mathematica

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];
Table[T[n, k], {n, 3, 16}, {k, 3, n}] // Flatten (* Jean-François Alcover, Sep 22 2021 *)

Formula

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