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

1,1

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.

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000720, A237658.

Sequence in context: A246112 A197780 A197611 * A290782 A367519 A002684

Adjacent sequences: A233460 A233461 A233462 * A233464 A233465 A233466

Keyword

nonn

Author

Farideh Firoozbakht, Feb 11 2014

Extensions

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

Status

approved