A233463 Numbers n such that the three numbers pi(n), pi(n^2), and pi(n^3) are prime.

6, 353, 804, 1175, 3482, 3570, 5062, 6217, 10663, 18055, 38712, 42297, 44976, 47626, 48132, 52166, 65611, 67353, 75699, 79864, 85094, 91723, 96057, 99161, 110008, 118551, 125829, 126017, 127286, 132545, 156376, 156694, 159295, 167129, 167366, 170938, 179290

Offset: 1

Author

Farideh Firoozbakht, Feb 11 2014

Keywords

• nonn

Comments

pi(k) is the number of primes less than or equal to k.

Next term is greater than 63117 and the Mathematica program given here could not find it.

Examples

			6 is in the sequence because the three numbers pi(6)=3, pi(6^2)=11, and pi(6^3)=47 are prime.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000720, A237658.

Programs

Mathematica

Do[If[PrimeQ[PrimePi[m]]&&PrimeQ[PrimePi[m^2]]&&PrimeQ[PrimePi[m^3]],Print[m]],{m,63117}]
Select[Range[11000],AllTrue[PrimePi[{#,#^2,#^3}],PrimeQ]&] (* The program generates the first 9 terms of the sequence. To generate more, increase the Range constant but the program may take a long time to run. *) (* Harvey P. Dale, Dec 27 2021 *)

PARI

isok(n) = isprime(primepi(n)) && isprime(primepi(n^2)) && isprime(primepi(n^3)); \\ Michel Marcus, Apr 28 2018

Extensions

a(17)-a(37) from Chai Wah Wu, Apr 24 2018