OFFSET
2,1
COMMENTS
T. D. Noe found no more values up to 10000 and agrees with my conjecture that this sequence is probably finite. This is related to Chen's Theorem: "Every 'large' even number may be written as 2n = p + m where p is a prime and m in A001358 is the set of semiprimes (i.e., 2-almost primes)" which itself is related to Goldbach's conjecture. However, we have no proof, merely the sense that it gets easier and easier to find more and more A014612(i) + A000040(j) = n decompositions as n increases.
EXAMPLE
MATHEMATICA
Rest@Complement[Range[1000], Union@Flatten@Outer[Plus, Select[Range[1000], PrimeOmega[#] == 3 &], Prime[Range[PrimePi[1000]]]]] (* Robert Price, Jun 16 2019 *)
CROSSREFS
KEYWORD
more,nonn,fini
AUTHOR
Jonathan Vos Post, Jun 16 2007
STATUS
approved