OFFSET
1,2
COMMENTS
The corresponding sequence with the restriction to primes removed is empty.
Wang shows that all but x^{9/20+e} members of this sequence up to x are congruent to 2 mod 3, for any e > 0.
There are no more terms < 10^7. - Donovan Johnson, Jun 27 2012
There are no more terms < 4*10^9. - Jud McCranie, Jun 09 2013
There are no more terms < 10^11. - Giovanni Resta, Jun 09 2013
REFERENCES
Wang Mingqiang, On sums of a prime, and a square of prime, and a k-power of prime, Northeastern Mathematical Journal 18:4 (2002), pp. 283-286.
PROG
(PARI) list(lim)=my(p1=vector(primepi(sqrt(lim-5.5)), i, prime(i)^2), p2=List(), v=List(), u=List([1, 3, 5, 7, 9]), t); for(i=1, #p1, for(j=i, #p1, t=p1[i]+p1[j]; if(t>lim, break, listput(p2, t)))); p2=vecsort(Vec(p2), , 8); for(i=1, #p2, forprime(p=2, lim-p2[i], listput(v, p2[i]+p))); v=select(n->n%2, vecsort(Vec(v), , 8)); for(i=2, #v, forstep(j=v[i-1]+2, v[i]-2, 2, listput(u, j))); Vec(u)
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Charles R Greathouse IV, Jun 21 2012
STATUS
approved