[seqfan] Prime sums from neighbouring terms

[Éric Angelini]

Hello SeqFans,
I'm working on this idea with my friend Jean-Marc Falcoz:
is it interesting for the OEIS? Look at the following sequence S:

S = 1,2,7,3,6,4,5,8,10,11,9,12,14,15,13,18,17,19,20,21,24,16,...

Pick any triplet of successive terms: there is only one way to build a prime by adding two out of the three integers of the triplet. (S is the lexicographically erliest sequence of distinct terms with this property).

Indeed the triplet 1,2,7 permits only to build the prime 3=1+2 as 1+7=8 (composite) and 2+7=9 (composite).

The triplet 2,7,3 permits only the prime 5=2+3 as 2+7=9 (composite) and 7+3=10 (composite).

The triplet 7,3,6 permits only the prime 13=7+6 as 7+3=10 (composite) and 3+6=9 (composite).
Etc. [follow this link to see some variants: https://bit.ly/2Q7UdKA]
Best,
É.