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A237260
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Least positive integer m < n with prime(prime(m)) + 2 and prime(n-m) + 2 both prime, or 0 if such a number m does not exist.
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3
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0, 0, 1, 1, 2, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 1, 2, 3, 4, 23, 6, 1, 2, 1, 2, 3, 4, 7, 1, 2, 1, 2, 3, 4, 7, 6, 1, 2, 1, 2, 1, 2, 3, 4, 1, 2, 3, 1, 2, 3, 4, 14, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 24, 1
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OFFSET
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1,5
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COMMENTS
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Conjecture: a(n) < sqrt(6*n)*log(3*n) for all n > 0.
We have verified this for n up to 5*10^5. Note that a(273) = 271 > sqrt(6*273)*log(2*273).
According to the conjecture in A218829, a(n) should be positive for all n > 2.
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LINKS
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EXAMPLE
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a(5) = 2 since prime(prime(2)) + 2 = prime(3) + 2 = 7 and prime(5-2) + 2 = 7 are both prime, but prime(5-1) + 2 = 7 + 2 = 9 is composite.
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MATHEMATICA
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pq[k_, m_]:=PrimeQ[Prime[k]+2]&&PrimeQ[Prime[Prime[m]]+2]
Do[Do[If[pq[n-m, m], Print[n, " ", m]; Goto[aa]], {m, 1, n-1}];
Print[n, " ", 0]; Label[aa]; Continue, {n, 1, 70}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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