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
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
Programs
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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
Comments