A237659 Primes p with pi(p) and pi(p^2) both prime, where pi(.) is given by A000720.

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}]

Crossrefs

Cf. A000040, A000290, A000720, A006450, A038107, A237656, A237657, A237658.

Sequence in context: A076330 A087658 A269840 * A350052 A078655 A052279

Adjacent sequences: A237656 A237657 A237658 * A237660 A237661 A237662

Keyword

nonn

Author

Zhi-Wei Sun, Feb 11 2014

Status

approved