login
Primes p with pi(p), pi(pi(p)) and pi(p^2) all prime, where pi(.) is given by A000720.
2

%I #13 Jun 01 2018 21:44:36

%S 59,127,709,1153,1787,9319,13709,19577,32797,35023,39239,40819,53353,

%T 62921,75269,90023,161159,191551,218233,228451,235891,238339,239087,

%U 272999,289213,291619,339601,439357,500741,513683

%N Primes p with pi(p), pi(pi(p)) and pi(p^2) all prime, where pi(.) is given by A000720.

%C This is a subsequence of A237659.

%C Conjecture: The sequence has infinitely many terms.

%H Chai Wah Wu, <a href="/A237687/b237687.txt">Table of n, a(n) for n = 1..1000</a> (n = 1..150 from Zhi-Wei Sun)

%e a(1) = 59 with 59, pi(59) = 17, pi(pi(59)) = pi(17) = 7 and pi(59^2) = 487 all prime.

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

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

%Y Cf. A000040, A000290, A000720, A006450, A038107, A038580, A237656, A237657, A237658, A237659.

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, Feb 11 2014