A056636 -id:A056636 - cp's OEIS frontend

A084564 Even numbers having no more than four partitions into two odd primes.

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 50, 52, 56, 58, 62, 68, 80, 88, 92, 98, 122, 128, 152

Offset: 1

Reinhard Zumkeller, May 30 2003

nonn

A002375(a(n)/2) <= 4.

Almost certainly there are no further terms. - David Wasserman, Dec 30 2004

Eric Weisstein's World of Mathematics, Goldbach Partition.
Index entries for sequences related to Goldbach conjecture

Cf. A084562, A084563.

Cf. A056636.

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

Original entry on oeis.org

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

Offset: 1

Gil Broussard, Jul 25 2008

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

			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

Cf. A056636, A061357, A077914, A117929.

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

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

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

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A084564 Even numbers having no more than four partitions into two odd primes.

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

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