A140955 - OEIS

%I #18 Sep 07 2022 15:48:12

%S 0,2,4,6,8,10,12,14,38

%N Even integers that do not have at least two partitions into 2 distinct primes.

%C If A056636(3) = 128 (as is conjectured), then 38 is the last term in the sequence. - _Charles R Greathouse IV_, Sep 07 2022

%e 8 is a term because 3+5 is the only sum of primes = 8.

%e 16 is not in the sequence because 16 = 3+13 and 5+11.

%e 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

%o (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 Cf. A056636, A061357, A077914, A117929.

%K fini,full,nonn

%O 1,2

%A _Gil Broussard_, Jul 25 2008

%E Offset changed to 1 by _Alois P. Heinz_, Sep 07 2022