[seqfan] [a(n)+a(n1)+a(n+2)] is prime BUT [a(n)+a(n+2]) is not

[Eric Angelini]

Hello SeqFans,
Does this seq S extend smoothly without backtracking?

Start S with a(1)=1 and extend S with the smallest unused integer
such that [a(n)+a(n1)+a(n+2)] is prime BUT [a(n)+a(n+2]) is not.

S=1,2,8,7,4,18,21,14,12,11,6,24,29,20,10,13,30,36,5,26,16,19,32,38,3,42,22,...

I guess S is the lexico-first permutation of the integers >0.
Best,
É.