OFFSET
1,3
COMMENTS
If the sequence has no zeros at least for sufficiently large n, then one can believe that, for a pair of sufficiently large semiprimes of the same parity {r,s}, there is a number k=k(r,s) such that either {r-k, s+k} or {r+k, s-k} is a pair of primes. Then, if a representation 2*n = r+s with, say, min{r,s} > log(n) is considered, then, at least for sufficiently large n, it is reduced to the Goldbach representation 2*n = p+q with primes p,q. It is natural to think that a Goldbach-like conjecture that at least every sufficiently large even number is a sum of two semiprimes could be proved more easily than the classic Goldbach conjecture (cf. Chen's theorem).
LINKS
Wikipedia, Chen's theorem
PROG
(PARI)
list(lim) = my(v=List(), t); forprime(p=2, sqrt(lim), t=p; forprime(q=p, lim\t, listput(v, t*q))); vecsort(Vec(v)) \\ From A001358
sp = list(1000); vector(#sp, n, k=1; while(!isprime(sp[n]+k) || !isprime(sp[n]-k), k++); k) \\ Colin Barker, May 31 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Apr 25 2014
EXTENSIONS
More terms from Peter J. C. Moses, Apr 28 2014
STATUS
approved