[seqfan] Prime hatred

[Eric Angelini]

Hello SeqFans,

« Build the lexicographically first sequence where no set
  of consecutive integers sums up to a prime »

I get:

S = 1,8,6,10,12,18,4,14,22,20,16,24,26,...

No prime in S, of course (a one-element set is possible)

Could it be possible that S is a permutation of A018252?
(the non-prime numbers)

At this point of S there is no odd integer (except "1")...

Best,
É.