

A237259


Least positive integer k < n such that prime(k) + 2 and prime(prime(nk)) + 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
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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

ZhiWei 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(32)) + 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, nk], Print[n, " ", k]; Goto[aa]], {k, 1, n1}];
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

ZhiWei Sun, Feb 05 2014


STATUS

approved



