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A237659
Primes p with pi(p) and pi(p^2) both prime, where pi(.) is given by A000720.
3
17, 41, 59, 109, 127, 157, 353, 367, 709, 1153, 1787, 3319, 3407, 3911, 5851, 6037, 6217, 6469, 8389, 9103, 9319, 10663, 13709, 14107, 14591, 15683, 18433, 19463, 19577, 20107, 21727, 23209, 27809, 29383, 32797, 35023, 36251, 36599, 38351, 39239
OFFSET
1,1
COMMENTS
This is a subsequence of A237658.
Conjecture: The sequence has infinitely many terms.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..600 from Zhi-Wei Sun)
EXAMPLE
a(1) = 17 with pi(17) = 7 and pi(17^2) = 61 both prime.
a(2) = 41 with pi(41) = 13 and pi(41^2) = 263 both prime.
MATHEMATICA
p[m_]:=PrimeQ[PrimePi[m^2]]
n=0; Do[If[p[Prime[Prime[k]]], n=n+1; Print[n, " ", Prime[Prime[k]]]], {k, 1, 1000}]
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Feb 11 2014
STATUS
approved