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

3,1

Comments

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

Links

Table of n, a(n) for n=3..93.

Eric Weisstein's World of Mathematics, Goldbach Partition

Wikipedia, Goldbach's conjecture

Example

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}}.

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

Crossrefs

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

Sequence in context: A159060 A021770 A004589 * A197690 A351692 A181840

Adjacent sequences: A354833 A354834 A354835 * A354837 A354838 A354839

Keyword

nonn,tabl

Author

Jean-François Alcover, Jun 12 2022

Status

approved