Sequence related to Goldbach Conjecture

[Ed Pegg Jr]

This reminds me of my unnecessary triangular number
sequence:

http://www.research.att.com/projects/OEIS?Anum=A068591

Any number is the sum of three triangular numbers (Gauss).
The 8th triangular number (36) seems nonessential for these
sums. After eliminating 8, the eleventh triangular number
seems to be nonessential.

8,11,16,17,23,24,29,31,36,38,41,43 ... (conjectured)

I assume that there is an effort to try to find the
nonessential primes, in terms of Goldbach.

--Ed Pegg Jr