This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A140955 #22 Jul 15 2025 11:02:09
%S A140955 0,2,4,6,8,10,12,14,38
%N A140955 Even integers that do not have at least two partitions into 2 distinct primes.
%C A140955 If A056636(3) = 128 (as is conjectured), then 38 is the last term in the sequence. - _Charles R Greathouse IV_, Sep 07 2022
%e A140955 8 is a term because 3+5 is the only sum of primes = 8.
%e A140955 16 is not in the sequence because 16 = 3+13 and 5+11.
%e A140955 The only ways to express 10 as a sum of two unordered primes are 3+7 and 5+5. In one of the sums the primes are distinct. Thus, 10 is in this sequence. - _Tanya Khovanova_, Sep 07 2022
%t A140955 Select[Range[0,100,2],Length[Select[Union/@IntegerPartitions[#,{2}],AllTrue[#,PrimeQ]&&Length[#]==2&]]<2&] (* _James C. McMahon_, Jul 15 2025 *)
%o A140955 (PARI) is(n)=if(n%2, return(0)); my(t); forprime(p=3, n\2-1, if(isprime(n-p) && t++>1, return(0))); 1 \\ _Charles R Greathouse IV_, Sep 07 2022
%Y A140955 Cf. A056636, A061357, A077914, A117929.
%K A140955 fini,full,nonn
%O A140955 1,2
%A A140955 _Gil Broussard_, Jul 25 2008
%E A140955 Offset changed to 1 by _Alois P. Heinz_, Sep 07 2022