A140955 Even integers that do not have at least two partitions into 2 distinct primes.

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

Offset: 1

Author

Gil Broussard, Jul 25 2008

Keywords

• fini
• full
• nonn

Comments

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

Examples

			8 is a term because 3+5 is the only sum of primes = 8.
16 is not in the sequence because 16 = 3+13 and 5+11.
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
		

Crossrefs

Cf. A056636, A061357, A077914, A117929.

Programs

Mathematica

Select[Range[0,100,2],Length[Select[Union/@IntegerPartitions[#,{2}],AllTrue[#,PrimeQ]&&Length[#]==2&]]<2&] (* James C. McMahon, Jul 15 2025 *)

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

Extensions

Offset changed to 1 by Alois P. Heinz, Sep 07 2022