A354836 Triangle T(n,k) where, if n-k and n+k are prime, T(n,k) = n+k is the greater term of a Goldbach partition of 2n into two odd primes, or zero otherwise.

3, 0, 5, 5, 0, 7, 0, 7, 0, 0, 7, 0, 0, 0, 11, 0, 0, 0, 11, 0, 13, 0, 0, 11, 0, 13, 0, 0, 0, 0, 0, 13, 0, 0, 0, 17, 11, 0, 0, 0, 0, 0, 17, 0, 19, 0, 13, 0, 0, 0, 17, 0, 19, 0, 0, 13, 0, 0, 0, 0, 0, 19, 0, 0, 0, 23, 0, 0, 0, 17, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 17, 0, 19, 0, 0, 0, 23, 0, 0, 0, 0

Offset: 3

Author

Jean-François Alcover, Jun 12 2022

Keywords

• nonn
• tabl

Comments

This sequence has the same structure as A354805, which could be considered as sort of its characteristic function.

Examples

			Triangle begins:
    3;
    0, 5;
    5, 0, 7;
    0, 7, 0, 0;
    7, 0, 0, 0,11;
    0, 0, 0,11, 0,13;
    0, 0,11, 0,13, 0, 0;
    0, 0, 0,13, 0, 0, 0,17;
   11, 0, 0, 0, 0, 0,17, 0,19;
   ...
Example: for n=11, row {11,0,0,0,0,0,17,0,19}, when stripped of its zeros and subtracted from 2n=22, gives the partitions {{11,11},{17,5},{19,3}}.
		

Links

• Eric Weisstein's World of Mathematics, Goldbach Partition
• Wikipedia, Goldbach's conjecture

Crossrefs

Cf. A085090 (main diagonal), A061397 (column k=0 prepended with (0,2)), A145091 (column k=1 prepended with (0,2,3,0)), A354805.

Programs

Mathematica

nmin = 3; nmax = 16;
T[n_ /; n >= nmin, k_ /; k >= 0] := If[PrimeQ[n-k] && PrimeQ[n+k], n+k, 0];
Table[T[n, k], {n, nmin, nmax}, {k, 0, n - nmin}] // Flatten