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 A237259 Least positive integer k < n such that prime(k) + 2 and prime(prime(n-k)) + 2 are both prime, or 0 if such a number k does not exist. 3
 0, 0, 2, 2, 2, 2, 3, 2, 2, 3, 5, 5, 7, 7, 2, 2, 3, 5, 5, 7, 7, 20, 10, 10, 2, 2, 3, 5, 5, 7, 2, 2, 3, 5, 5, 7, 7, 35, 10, 10, 17, 2, 3, 20, 5, 17, 7, 35, 20, 10, 28, 28, 13, 41, 26, 26, 17, 28, 35, 20, 2, 3, 33, 5, 2, 3, 2, 3, 10, 5 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A000040, A001359, A006512, A218829, A237260. Sequence in context: A184721 A134868 A322861 * A235614 A127417 A308622 Adjacent sequences:  A237256 A237257 A237258 * A237260 A237261 A237262 KEYWORD nonn AUTHOR Zhi-Wei Sun, Feb 05 2014 STATUS approved

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Last modified May 26 17:16 EDT 2022. Contains 354092 sequences. (Running on oeis4.)