OFFSET
1,1
LINKS
J. Stauduhar, Table of n, a(n) for n = 1..380
EXAMPLE
4, 6, 8, and 12 have just one Goldbach partition each, so the sum of the lesser and greater elements of each partition is prime, giving the first four terms in the sequence.
Three Goldbach partitions comprise 22: (3,19), (5,17) and (11,11). 3 + 5 + 11 = 19, and 11 + 17 + 19 = 47. Both 19 and 47 are prime, so a(5) = 22.
MATHEMATICA
f[n_] := Module[{lst={}}, For[i=2, i<=n, i+=2, parts=Select[ IntegerPartitions[i, {2}], And@@PrimeQ /@#&]; If[And@@PrimeQ[Plus@@parts[[Range[1, Length[parts]], {1, 2}]]],
AppendTo[lst, i]]; ]; lst]; f[1000](* J. Stuaduhar, Sep 18 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
J. Stauduhar, Sep 16 2012
STATUS
approved