First differences are primes

[Eric Angelini]

Hello,
could someone please extend this (if of interest for the OEIS) :

S = 1 4 6 25 30 77 84 95 108 125 148 177 208 245 286 329 382 441 502 573 640 713 792 875 964 1065 1162 ...

Definition :

« Non-primes sequence whose first differences show all primes, once »

The sequence S is build like this :

Start with 1:

S = 1

Add the smallest prime not added so far, in order to get a composite:

- Can we add 2? No, because 1+2=3 and 3 is prime
- Can we add 3? Yes, because 1+3=4 and 4 is composite

So we have now:

S = 1,4,

Add the smallest prime not added so far in order to get a composite:

- Can we add 2? (smallest available prime); yes, because 4+2=6 and 6 is composite

So we have now:

S = 1,4,6

- Can we add 5? No, because 6+5=11 and 11 is prime
- Can we add 7? No, because 6+7=13 and 13 is prime
- Can we add 11? No, because 6+11=17 and 17 is prime
- Can we add 13? No, because 6+13=19 and 19 is prime
- Can we add 17? No, because 6+17=23 and 23 is prime
- Can we add 19? Yes, because 6+19=25 and 25 is composite

So we have now:

S = 1,4,6,25

- Can we add 5? (smallest available prime); yes, because 25+5=30 and 30 is composite

S = 1,4,6,25,30

etc.

Best,
É.

(I'm working on seq. T :
 « Primes sequence whose first differences show all non-primes, once »
   Hope this one is not in the OEIS either)