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

1,1

Comments

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

For primes in this sequence, see A237659.

Links

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

Example

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.

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}]

Prog

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

Crossrefs

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

Sequence in context: A096426 A130051 A338894 * A301696 A301727 A038795

Adjacent sequences: A237655 A237656 A237657 * A237659 A237660 A237661

Keyword

nonn

Author

Zhi-Wei Sun, Feb 10 2014

Status

approved