%I #21 Apr 28 2018 03:40:32

%S 6,17,33,34,41,59,60,69,109,110,111,127,157,161,246,287,335,353,367,

%T 368,404,600,709,711,713,718,740,779,804,1153,1162,1175,1437,1472,

%U 1500,1526,1527,1679,1729,1742,1787,1826,2028,2082,2104,2223,2422,2616,2649,2651

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

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

%C For primes in this sequence, see A237659.

%H Chai Wah Wu, <a href="/A237658/b237658.txt">Table of n, a(n) for n = 1..10001</a> (n = 1..3000 from Zhi-Wei Sun)

%e 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.

%t p[m_]:=PrimeQ[PrimePi[m]]&&PrimeQ[PrimePi[m^2]]

%t n=0;Do[If[p[m],n=n+1;Print[n," ",m]],{m,1,1000}]

%o (PARI) isok(n) = isprime(primepi(n)) && isprime(primepi(n^2)); \\ _Michel Marcus_, Apr 28 2018

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

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, Feb 10 2014