If the sequence contains no perfect squares>4, then the Goldbach conjecture in Fermi-Dirac arithmetic (FDGC) is true (see comment in A241927).
Essentially, the sequence is the Fermi-Dirac analog of A100570. Since A100570 is conjecturally finite, it is natural to suppose that this sequence is also finite.
There is not another term up to 10^6. - Peter J. C. Moses, May 05 2014
Thus, if 20 is the last term of the sequence, then the FDGC is true. - Vladimir Shevelev, May 05 2014