A237658 Positive integers m with pi(m) and pi(m^2) both prime, where pi(.) is given by A000720.

6, 17, 33, 34, 41, 59, 60, 69, 109, 110, 111, 127, 157, 161, 246, 287, 335, 353, 367, 368, 404, 600, 709, 711, 713, 718, 740, 779, 804, 1153, 1162, 1175, 1437, 1472, 1500, 1526, 1527, 1679, 1729, 1742, 1787, 1826, 2028, 2082, 2104, 2223, 2422, 2616, 2649, 2651

Offset: 1

Author

Zhi-Wei Sun, Feb 10 2014

Keywords

• nonn

Comments

The conjecture in A237657 implies that this sequence has infinitely many terms.

For primes in this sequence, see A237659.

Examples

			a(1) = 6 since pi(6) = 3 and pi(6^2) = 11 are both prime, but none of pi(1) = 0, pi(2) = 1, pi(3^2) = 4, pi(4^2) = 6 and pi(5^2) = 9 is prime.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10001 (n = 1..3000 from Zhi-Wei Sun)

Crossrefs

Cf. A000040, A000290, A038107, A237595, A237656, A237657, A237659.

Programs

Mathematica

p[m_]:=PrimeQ[PrimePi[m]]&&PrimeQ[PrimePi[m^2]]
n=0;Do[If[p[m],n=n+1;Print[n," ",m]],{m,1,1000}]

PARI

isok(n) = isprime(primepi(n)) && isprime(primepi(n^2)); \\ Michel Marcus, Apr 28 2018