OFFSET
1,1
COMMENTS
Conjecture: a(k) is prime for k > 3. Tested for k up to 3*10^4.
LINKS
Eric Weisstein's World of Mathematics, Goldbach Partition.
EXAMPLE
For k = 4, 2k = 8. The number of the distinct Goldbach parts of 8 (3 and 5) is prime, therefore 4 is in the sequence.
5 is in the sequence because the 2 = A045917(5) Goldbach partitions of 10 are 5 + 5 and 3 + 7, and there are 3 distinct parts, namely 3, 5 and 7. - Wolfdieter Lang, Feb 23 2015
MATHEMATICA
lstIn={}; lstFin={};
goldPart[x_]:=Module[{h=x/2}, While[h>1, If[And[PrimeQ[h], PrimeQ[x-h]], AppendTo[lstIn, {h, x-h}]]; h--];
lstFin=Length[Union[Flatten[lstIn]]]; lstIn={}; lstFin];
a254713=Flatten[Position[PrimeQ[goldPart/@Range[2, 2002, 2]], True]]
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Ivan N. Ianakiev, Feb 06 2015
EXTENSIONS
Edited. Wolfdieter Lang, Feb 23 2015
STATUS
approved