OFFSET
1,3
COMMENTS
Conjecture: a(n) < 2*sqrt(n)*log(3*n) for all n > 0.
We have verified this for n up to 5*10^5. Note that a(202) = 173 > 2*sqrt(202)*log(2*202).
According to the conjecture in A218829, a(n) should be positive for all n > 2.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
Z.-W. Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014
EXAMPLE
a(3) = 2 since prime(2) + 2 = 5 and prime(prime(3-2)) + 2 = prime(2) + 2 = 5 are both prime, but prime(1) + 2 = 4 is composite.
MATHEMATICA
pq[k_, m_]:=PrimeQ[Prime[k]+2]&&PrimeQ[Prime[Prime[m]]+2]
Do[Do[If[pq[k, n-k], Print[n, " ", k]; Goto[aa]], {k, 1, n-1}];
Print[n, " ", 0]; Label[aa]; Continue, {n, 1, 70}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Feb 05 2014
STATUS
approved