A237687 Primes p with pi(p), pi(pi(p)) and pi(p^2) all prime, where pi(.) is given by A000720.

59, 127, 709, 1153, 1787, 9319, 13709, 19577, 32797, 35023, 39239, 40819, 53353, 62921, 75269, 90023, 161159, 191551, 218233, 228451, 235891, 238339, 239087, 272999, 289213, 291619, 339601, 439357, 500741, 513683

Offset: 1

Author

Zhi-Wei Sun, Feb 11 2014

Keywords

• nonn

Comments

This is a subsequence of A237659.

Conjecture: The sequence has infinitely many terms.

Examples

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

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..1000 (n = 1..150 from Zhi-Wei Sun)

Crossrefs

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

Programs

Mathematica

p[m_]:=PrimeQ[PrimePi[m^2]]
n=0;Do[If[p[Prime[Prime[Prime[k]]]],n=n+1;Print[n," ",Prime[Prime[Prime[k]]]]],{k,1,1000}]