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)