OFFSET
1,3
COMMENTS
According to Chen's result, the terms of this sequence are positive, at least for sufficiently large n.
REFERENCES
J. R. Chen, On the representation of a large even integer as the sum of a prime and the product of at most two primes, Kexue Tongbao, 17(1966), 385-386.
J. R. Chen, On the representation of a larger even integer as the sum of a prime and the product of at most two primes, Sci. Sinica, 16(1973), 157-176.
P. M. Ross, On Chen's theorem that each large even number has the form (p1+p2) or (p1+p2p3), J. London Math. Soc. (2) 10(1975), 500-506.
LINKS
Peter J. C. Moses, Table of n, a(n) for n = 1..10000
FORMULA
For n >= 2, a(n) = Sum_{3<=p<=n, p prime} A(2*n - p) + Sum_{t<=2*n, t odd semiprime} A(2*n - t) + A(n) - binomial(A(n),2) + delta(n) - a(n-1) - ... - a(1), where A(n) = A033270(n), delta(n) = 1, if n is prime, and delta(n) = 2, if n is a composite number. - Vladimir Shevelev, Jul 11 2013
MAPLE
A155216 := proc(n) local a, p, q, twon ; twon := 2*n ; a := 0 ; for i from 1 do p := ithprime(i) ; if ithprime(i) > twon then break; end if; q := twon -ithprime(i) ; if isprime(q) and q>= p then a := a+1 ; end if; end do: for i from 1 do p := ithprime(i) ; if ithprime(i) > twon then break; end if; q := twon -ithprime(i) ; if isA001358(q) then a := a+1 ; end if; end do: return a; end proc: seq(A155216(n), n=1..80) ; # R. J. Mathar, Jul 26 2010
MATHEMATICA
a[n_] := Module[{k = 0, p, q}, For[i = 1, True, i++, p = Prime[i]; If[p > 2n, Break[]]; q = 2n - Prime[i]; If[PrimeQ[q] && q >= p, k++]]; For[i = 1, True, i++, p = Prime[i]; If[p > 2n, Break[]]; q = 2n - Prime[i]; If[ PrimeOmega[q] == 2, k++]]; k];
Array[a, 80] (* Jean-François Alcover, Nov 28 2017, after R. J. Mathar *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Jan 22 2009
EXTENSIONS
Terms beyond a(21) from R. J. Mathar, Jul 26 2010
STATUS
approved